The touch id is very sensative on these phones. Failure could be caused a few different ways. The most common would be.
1) The home button was not replaced with the original button. The button and logic board are paired at "birth" and they can only speak to each other.
2) The flex cable is very sensative. If the button was removed, it may have damaged a small trace in the cable. The connection may not be well seated. Try removing it, cleaning them, and reconnecting.
3) The heat required from a touch ic repair is know to cause a few different side effects. Although I haven't seen touch id fail, I wouldn't say it's impossible. Heating up a board like that can cause random components to short out or fail.
If you are sure that the button is original, and then have ensured clean connections, honestly I would just stop there. Trying to track down whatever else might be causing this is just a time sucking rabbit hole. Its not worth gaining a secondary function on your phone.
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