I just spent 30 minutes trying to reconnect my chain.

I needed to take out a few links, I popped out two pins using the chain tool, took one of the pins and tried to push it back in. This is an extremely delicate work, to put it mildly. The pin is just thick enough that I can't push it into the hole by hand. I need to hold the chain sideways, balance the pin on top of the hole, put on the chain tool and try to push it in. The pin is slippery and tends to fall to one side from any vibration. Even if I manage to squeeze it between the chain tool and the chain, 9 times out of 10 it goes in crooked and I have to start over.

I can't imagine doing this at the side of the road in the event of a malfunction. More to the point, I can't imagine a mechanic doing this in a bike shop. I have a SRAM 10-speed chain and I can buy new "master links" which cost $16 for a 4-pack on Amazon (which is unreasonable since I can get a brand new chain for $27). My chain tool (Park Tool CT-5) does not seem to offer any functionality that would make pushing pins into the chain any easier. What am I missing?

Master links are so much easier. 10 seconds and off you go.

Did you push the pin out entirely ? You should leave it in the side plate, with a tiny bit protruding to the inside so you can line it up with the hole.

As I recall, my KMC chains come with the link, so no extra purchase needed.

You're making a case for spending the few bucks for a quick link, but I think your error lies in pushing the pins all the way out. Normally, you leave the pin in the outer plate. I haven't had to do this since switching to quick links, but I don't recall having much problem in the past.

Most 7/8, 9, 10, and 11 spd chains do not have pins that can be reused, and even if a chain does have those, you don't push the pin all the way out of the side plate when you break the chain. Your chain was most likely connected with a Sram reusable link (Powerlock, I think it's called), and you were supposed to open the chain at that link and remove extra links from one of the ends, then re-connect using that link. The four pack on Amazon would probably last you through two to four chains, depending on how often you take your chain off to clean and lube. Bottom line, don't use a tool until you learn how (through being shown, reading, or watching tutorials). You need to get another Sram reusable link to put your chain back together.

Grab a section of old chain and practice using your chain tool. You will soon find that point at which links pop but the pin stays inside the side-plate. If the pin is protruding very slightly inside, it will seat into the inner link when you re-assemble.
Use a bit of wire as a hook to give some slack in the chain as you fix it back together.
Putting pins back is a major PITA. Most chains have a few extra links, you should alway keep these for such emergencies. Take the pinless link out altogether and replace it with a link from your spares, with the pin in-place.
The easiest way is to use a master-link which needs no tool but that costs a little bit.

Modern chains from 7/8-speed and narrower should never reuse a pin, even if you don't push it all the way out. Their pins are flared or riveted at the ends and pushing out even one side wipes off the flair and reams the hole larger. When you push it back in you create a weak spot that is very likely to fail under load. If you have to break and rejoin a chain you use the specific joining pin (Shimano) or a master link (SRAM, Wippermann, KMC).

Frankly, I'm a bit surprised the above posters even mentioned only pushing a pin part way out and reseating it. You do not reuse a regular pin.

I mentioned pushing the pin out partway because I was having an old-school flashback.
I have only used master links since going modern.

Neither a mechanic nor someone who had looked at instructions for chain replacement would do that. I would suggest that the next time you do a procedure that you look it up first. Other than that the advice you need has been posted.

As for the cost of master links, you just wasted 30 minutes of your time for lack of a master link - what is that worth? Of course you're welcome to look for a cheaper source for the master links or just ride a chain until you replace it, but your concern about the cost of something in that price range, that is used once or twice a year, seems misplaced.

Sram Powerlock is not reusable. It says so right in the manual that comes with the chain. I quote: "The Power-Lock is for one-time use only! Always use a new PowerLock when fitting a new chain. Once the PowerLock is installed it can only be removed by means of a chain tool." I spent some time trying to open the master link a while back and confirmed that it could not be opened by hand. If I shorten the chain and then some time later I want to lengthen it again, I'm apparently supposed to use two master links in one chain.

P.S. So, the bottom line is that (at least with SRAM) the chain tool can only be used to break the chain, and I need to get a new master link every time I want to reconnect it?

According the SRAM, yes. Single use only. I've removed them to clean chains and re-used them (Park makes a tool specifically to remove quick links ) on the same chain. KMC makes reuseable links, but I'd always replace them when installing a new chain. If you're going to replace the chain because it's worn, don't re-use the most important link...cuz it's worn too.

KMC makes both reusable and single use 10 speed links. They are identified on the package. You can use the KMC link on KMC, SRAM or Shimano chains. You can buy a card of 6 or so and carry a spare for your friends who break chains. The links make it easy to remove the chain for cleaning. The Park tool is nice to have.

SRAM claims their 10-speed links are not reusable but I've read about many riders who have reused them successfully and have also read SRAM makes that claim to avoid a patent infringement claim.

Hamster - $8.73 for 6

https://www.amazon.com/gp/product/B00...=ATVPDKIKX0DER

you can also buy a wipperman reusable link.

There's a review right on the front page saying that it's incompatible with SRAM.

Interesting. I've had two different SRAM chains on my bike, KMC is currently on there and I'm about to swap it out for an ultegra chain (got one cheap). I always thought all three were largely interchangeable. Good to know they're not!

AFAIK, KMC is the OEM for all 3 brands.

Found this while I was looking for other information about chain cleaning: (On the KMC website, take it for what it's worth)

IS KMC MISSING LINK COMPATIBLE WITH SHIMANO CHAIN, SRAM CHAIN, OR CAMPY CHAIN?
Yes, KMC constructs Missing Link I, II, 9, and 10 for 7.3mm, 7.1mm, 6.6mm, and 5.9mm respectively; all Missing Links are compatible with Sram, Shimano, and Campy equivalent chains.

Unless I'm misreading this, the OP isn't even using a chain tool (how did he get the pins out,hammer and punch?)