I found some material on this issue. One is make sure "Emulate Touchscreen" is enabled in the settings which seems to be a common one. Another is a scaling issue that seems version related and the last is a hidden layer blocking the inputs with code examples. Hope this helps!
https://www.reddit.com/r/godot/comments/91gdlk/touchscreen_input_on_area2d_not_w...
https://godotengine.org/qa/22834/touchscreenbutton-not-working