This recently started acting funny. Tapping hardly works and raising stopped all together. Push button and screen comes on and goes off like it was on when I pushed the button.
Not sure I understand what you mean by the last sentence, but have you ensured "Raise to Wake" is still enabled under Settings > Display & Brightness > Raise to Wake AND that "Tap to Wake" is enabled under Settings > Accessibility > Touch > Tap to Wake?
If that doesn't do it, then try restarting your iPhone: