Have experienced this occasionally on my series 4. I believe it's an issue with WatchOS 6.1 as I never experienced this prior to updating.
Anyway, I've managed to work around the glitch by force quitting the Timer app (thus avoiding the need to restart the watch, or as the OP is doing uninstalling/reinstalling the app).
You can force close the app by holding down the side button (not the digital crown) while the timer is active. Once it changes to the shut off screen, press and hold the digital crown button until it returns to the home screen. You should now be able use the Timer normally again.
Hopefully Apple fixes the issue so we don't need to apply these workarounds.