My rear Ultegra brake stays partially on after i hit the rear brakes. like when i squeeze it the spring or whatever doesn't open the calipers back up again. Does this just mean my cable is shot or can i adjust something to make them open back up? I can manually push the middle "arm" of the brake that is attached to the cable back down and they open up but that is risky while riding.

Determine why it is binding. Is the cable sticking, or is it the brake?

The cable could be gunked up/rusted in the housing and the additional friction of the gunk/rust is stronger than the spring that's supposed to return the brake to the open position.
OR
The spring is too weak to do its job of returning the brake to the open position. I don't know--do springs get tired and lose their springiness?
OR
The bolt that holds the whole thing together is adjusted too tight, causing friction which prevents the spring from doing its job.

disclaimer: I've never even seen an ultegra brake in rear life--these are generic problem/solutions.

Haha--no guts no glory!! (Actually I can't even envision somebody doing this--maybe Plasticman)

Yea, when i get back from my ride today i will probably take the whole brake off and see if i can clean it up and see if that helps.

this is the type of brake i'm talking about. (and reaching back to push down the arm isn't all that difficult.. but it is kinda close to moving parts so i'd rather not)

Hold on a second.

Before you take major repair or replacement steps do the simplest thing first...put some lube on all the pivot (moving) points of the caliper then operate the brake several times and see it that frees it up. If not then try loosening the pivot bolt head while holding the rear mounting nut in a fixed position, just loosen about 1/16ths of an inch then test again, if it works better but still a bit stiff then loosen the nut again about 1/16ths of an inch and retest.

Here's a site that shows detail pics on how to adjust the caliper: https://www.parktool.com/repair/readhowto.asp?id=22

+10 to that. 99% of the time, it just needs a little tiny bit of lube on the pivot points. Work it in quite well and you'll probably be fine.

check for friction in cable /housing. is the housing kinked?

I'll give this a shot. I do ride in a fairly sandy and sometimes wet area (RI) so it might just need to be lubed up a bit

Do the pivot point lube first. If it's still stuck:

Unbolt the cable at the clamp. Then squeeze the brake pads to the rim and release. Does it spring back without the cable attached? If it does, the problem is in the cable.

Isolating a binding brake is fairly straighforward, most of which is reflected in the various answers above.

First loosen the cable at the calipers until they move all the way out from the rim. Remove the cable from the binding bolt but leave the housing in the barrel.

Second, push the two pads to the rim and release. They should offer a fairly large amount of resistance and spring right back when released. If not the pivots are tight or corroded. I doubt very much that lack of lubrication alone would cause calipers to not release.

If the calipers move freely check the cable. Hold onto the cable with one hand, about an inch from where it emerges from the barrel. Pull on the brake lever with your other hand - it should move very easily back and forth. If you don't have aero or sti style brake lever you can easily disengage the other end of the cable from the lever temporarily and move it that way. If it moves with difficulty remove the entire cable and check for dryness and corrosion. If there is ANY corrosion replace the cable and housing and use a light machine oil or teflon lube when you reinstall. Just because modern housings are lined with teflon does not mean the cable will not corrode - small spaces easily harbor water vapor.

If cable and caliper are fine that leaves the lever. It should always move VERY easily. If it does not there are various reasons it could bind. Too much to go into here, but careful inspection should tell you the problem. Good luck!

Instead of reaching back and opening the caliper while riding, grab the brake cable under the top tube, then pull the brake cable towards the back of the bike.

My rear Ultegra does the same thing. I have narrowed it down to where the ferrule on the brake cable meets the cable guide braze ons on the frame. The braze ons are too large for the ferrule, the ferrule can angle sideways and the cable get's pinched between the braze on and the opening to the ferrule. Too much friction for the return spring to overcome. I get slack in the cable under the top tube. THis helped me figure out where it was binding.

I discussed this with theh LBS and they said I could, with the ferrule in the braze on GENTLY squeeze it with pliers to pinch the braze on enough to hold the ferrule snugly.

I haven't done this yet because I don't want to crack the braze ons off the frame. I also may look for a larger diameter ferrule or one with a thicker wall.

I get the saggy cable under the top tube also so i think i might be in the same boat. I did go lube up the joints and dripped some lube into the housing and that has at least improved things so that the calipers will open up far enough to not rub so i'm ok with it for now. I would like to find bigger housing so that the sagging cable issue is solved also.

I have an old Schwinn Varsity that does that. I've learned to hum songs in my head whose beats match the tempo of the wheel rotation.

Problem solved.

I'm not so sure that is the problem/solution, as I'm not sure what you mean by "saggy cable," so it's not clear it's the same problem. Again, the best way to diagnose is to isolate the components. If there are housing sections from the brake lever to the top tube and from top tube to the rear brake then checkk each section by loosening the cable and moving each section back and forth by hand. Too much friction can also be caused by the housing being either too short or too long. Should have a gentle curve, neither stretched nor looped out.

I unhooked the cable and squeezed the calipers manually. they were a bit rough but got better with some lube. then i unhooked the rear housing and lubed up each end and the adjustment screw interior where it runs through. now when i squeeze the brakes the caliper operate properly but i get slack in the cable along the top tube and the front housing is loose enough to pull out of the braze on after squeezing the brake lever. front housing issue?

Cable too loose in the housing. Needs to be quite tight, making sure all ferrules are properly seated along the entire length. This can be a little tricky--if you don't have a "third hand tool" is easy enough with pliers or vice grips, hex-head wrench, etc. placed where you can reach them while holding the cable. Your problem probably came about by one of the ferrules slipping out of its housing or a section of cable housing slipping out of the ferrule while you were juggling the tools trying to tighten the brake. Seemed tight enough at first, then when the cable components slipped back into proper alignment, you got a case of (blush) saggy cable.
https://www.sheldonbrown.com/cables.html

Well i think i have it mostly fixed.. i replaced and slightly shortened the rear housing section and it seems to be working better now. hopefully it stays that way

Just put a bit of tape around the ferrule to increase its diameter; easy.

Did that. The (electrical) tape made it worse. The tape is soft and can get crushed. At this point I am just living with it. I am about ready to do the yearly-ish cable replacement. I can cut the rear housing a bit longer, I think this is also exacerbating the problem as the rear housing may not be hitting the rear cable guide at the right angle.

I am at the point where I just need to start over and have been too lazy to do it. Oh, and now racing is picking up so I don't know when I can get it done. Ah, the life of a procrastinator.

Yes, I think I really said that.

Yes, that probably is at least part of the solution. if the cable is loose under the top tube that would mean that the brake is unable to pull the cable through the REAR housing or ferrules, or that the caliper is not moving freely. When you release the brake lever the operation of the brake is now occuring from the brake caliper back to the lever - the reverse of when you apply the brakes.

Unless I missed it, did anyone mention adjusting the calipers so they are centered on the wheel before activating the brake? I've seen brakes so badly off-center, that one side is nearly in contact with the rim, while the other has a huge gap. There's a tiny allen bolt (1.5mm?) on the top of the arm that can be turned in order to move the calipers so they can be centered on the wheel.

Mos6502 is right; first determine which part is binding. Assuming the brake caliper is okay, check for any burrs on the ends of the brake housings that were not cleaned up properly after the housings were cut - they will impede smooth motion of the cable. Also, check the overall condition of your brake cables & housing: any rust, worn housings, a crimp in the cable, or even sometimes a hidden broken cable strand will all affect the rear brake's performance.

Rode yesterday and had a few hard full braking with both front and rear and the rear opened right back up again and not as much cable sag on the TT so i think the rear housing was most of the issue. shift cables and housing are next but i'll wait until into summer to avoid the spring rains.