I've been hanging on to my iPhone 4S for this very reason. The battery is nearly shot after 4 years, but I would call that a pretty good run by today's standards (Take that, planned obsolescence!).
You can replace the battery. The removal is a bit frightening (there's a shit-ton of glue so you're tearing the battery apart to get it out), but aside from that it's a 10mn~15mn job (first time, being careful), did that on my own 4S. Biggest annoyance (aside from fear of piercing the battery while you're tearing it out) is some sort of pressure/spring-loaded contact inside which is a pain to get back in place.
ifixit sells complete replacement kits (battery + plastic forcing tool + pentalobe driver + replacement philips screws) for $25, or just the battery for $20, you can probably find even cheaper parts elsewhere.
I've changed my battery twice already on 4S. There isn't shit ton of glue, but two strips that remove fairly easily.
I would keep the device and wait for iPhone 7, but lack of RAM makes the use beyond basic a pain. Even some basic stuff lags ridiculously (opening Music and navigating to your playlists now takes up to a minute). Forget multitasking beyond 3 apps. With two are always gaming whether app will come back from memory or storage.
Apple is really evil in this sense. The sub par amounts of RAM are forcing us to upgrade quicker than it should be. And so many people (even tech) are rejecting the idea that RAM is needed on iOS.
The biggest problem for me hasn't been the battery but the sluggishness of iOS8 on a 4S. There are times when it simply won't react to touch input anymore for a while. Some bugs have accumulated as well - my alarm clock won't go off anymore (timer still always works, even over night, strangely enough), sound output is sometimes broken until I open up "Music" to sort of reinitialize it, the lockscreen is sometimes frozen etc. It's been barely usable but I've held on. Sad there is no iPhone mini.
I believe they're using removable adhesive strips these days, similar (if not identical) to 3M's Command line. Long story short, if you're "tearing" anything, you're doing it wrong. Pull on the exposed end of the strip and the adhesive will detach cleanly, leaving no residue.
Good luck with that, the pulltab was a useless piece of junk and it most definitely did not detach anything (let alone cleanly). I very much would have liked it to work, it would have been significantly less stressful than having to leverage the plastic tool on the metal sides of the phone to tear out the battery.
Yeah, the pulltab is less than useful. It took a worryingly large amount of force to get the battery unstuck and pulling the tab folded it into a neat U shape. Having seen plenty of exploding battery videos I was expecting the thing to go up at any second.
ifixit sells complete replacement kits (battery + plastic forcing tool + pentalobe driver + replacement philips screws) for $25, or just the battery for $20, you can probably find even cheaper parts elsewhere.
Phone resurrected, money well spent.