There are 2 more possibilities in addition to iBar's suggestions:
1/ I'm assuming that you are properly tightening the 2 screws that hold the power button bracket (without damaging the screen assembly flat cables);
2/ You said you replaced the button itself. If you mean the metallic button, then disassemble again, and put back the original button. First because that button doesn't fail (unless it was physically damaged somehow), second because if you flip it and look at the bottom/back, you'll see a small round piece of metal without which the button will not click when re-assembled. That cylinder is probably missing from the new button.
If you want to keep the new button, transfer that small cylinder. I bend or partially cut the old button with pliers to make the cylinder stick out, then I grab it with fine tweezers.
Be prepared to see that cylinder fly away though, so work in an area where it will be possible to find it if this happens.
Let us know what helped and good luck.
Also, you mentioned that you need to put your phone in restore mode to fix it (why's that?). You can do that without a working power button in some cases:
A/ If your iPhone is turned OFF, press and hold the Home Button, and at the same time connect your iPhone to your laptop. It will start in Restore Mode, given that the battery is connected and is holding a charge.
B/ If your iPhone is ON, and you can have access to Settings>General>Accessibility>Assistive Touch (turn it ON), then press Assistive Touch>Device>and keep pressing until you get the Swipe-to-Turn-Off. Once done, follow step A here above.
4 
3 
89 
