Funny...... we were camping this weekend and the same thing happened. I went to a local RV Supply store and bought a new faucet assembly ($31). I just got home and did some research, Amazon has one that is all Stainless steel and should eliminate this issue.
https://www.amazon.com/G-Sunny-Showe...zcF9hdGY&psc=1
The other way to go is to keep a spare:
https://www.amazon.com/dp/B085MB6BXB...opcQF3BEi&th=1