iPhone 4s replaced battery, still drains quickly
The only thing I could recommend for an older Apple device is to call Apple Support and have them run diagnostics on the device (or you can visit a store). 

Worst case scenario, the only thing that may be the culprit is the logic board. Apple no longer has those so you may need to contact an Apple Authorized Service Provider and see if they can order the parts or find someone that could be selling the parts.