An Uber driver needs to be able to cover gas out of their pay plus make enough extra to effectively receive a decent wage. If gas prices go up but the price of an Uber fare (and subsequent payout) does not, then it becomes uneconomical for people to drive for Uber and they stop doing it.

Other than when Uber deeply discounts to drive growth, it's always been cheaper to drive yourself than to pay Uber. The reason you pay Uber is for other reasons (e.g. convenience, cost of parking, being away from your vehicle, intoxication).