My back rim brakes keep shifting out of alignment. I'll start the ride with them aligned, but end it with one end touching the wheel. I've tightened where the breaks and frame, but no luck. The wheel is true. Any suggestions?

Is the cable housing too long such that it pushes the caliper out of center?

I presume that when you are centering them you are first loosening the back nut, center them and then re-tighten. Also your front nut/locknut may be to tight and therefore binding

Check out this Park Tool Video, centering adjustment starts around 8:23

Thanks for the help. I wasn't able to figure it out on my own, but my friend seems to have done something that is working...

Depending on the caliper, there is normally a way to adjust the spring tension so that each arm pulls away from the wheel equally. If you have a photo of the calipers, we may be able to see how to adjust this, usually a little screw on one or both arms.

I am at a loss of what to do. I've taken it to the shop and they said it looks fine. After my first post-shop ride, the problem came back.

I am wondering if maybe the cable housing is pushing the caliper as tfunk suggests. The break always shifts to the right. How would I know/check?

Are your front and rear calipers the same (other than the bolt)? If so, try swapping them; that might help narrow down whether it's internal in the caliper itself, vs. something to do with how it's mounted.

Thanks for the good idea! They look the same.

By shifting to the right do you mean the right pad touches or the left?

I don't know how your cables are routed but on older top tube routed cables you can usually move the cable through the eyelets or clamps a little bit and the friction will keep them where you moved them to. The movement/cable location changes the pressure exerted on the rear brake. If you mess with that and see how it changes things you should be able to figure it out.

The left pad ends up touching.

That is consistent with a slightly too long cable looking at the picture. This is based my assumption that the cable attachment triangle is connected to the arm that holds the left brake pad.

Try moving the cable a little a time so that it has more slack at the bars, less slack going behind the seat post. Squeeze and let the lever spring back a couple times to see where it comes to rest and whether or not is an improvement.

Is your wheel true? If not there is your problem. Also, if your spokes aren't at the correct tension, then your rim might be staying somewhat true but anyone's guess where they will be while in motion with a load on them.

There is an adjustment screw on those brakes to shift where they center. It's the little 3mm hex that is described in instruction number 1 on page 34 of this:
https://www.servicearchive.sram.com/...nual-rev-a.pdf
might not be exactly the same as your year model but it's similar.

Thanks for the advice.

Just had the wheels trued--same problem. I presume the mechanic would have said something if the spokes weren't at the right tension?

I have been adjusting that screw.

I pulled the cable through a bit to the front like you recommended. Will see how it goes when I next take it for a longer ride.

Before the long ride you should mark the cable's position with something (like a marker or ring of tape next to something that is fixed). If the problem comes back when the cable shifts that confirms the cable is the issue.

^^^^ +1, and if possible, mark the position of the adjuster screw; maybe it is what is moving out of position.