So I'm not sure what's going on. Remote start works fine. But when I change to Run error message either tells me key fob not located or touch key fob to start button. If it were a key fob battery issue wouldn't the remote start fail to operate?
Not sure about specifics but have you changed the battery (in the key fob) since you got the vehicle? Looks like you have a 2022. A real cheap "attempted fix" of a new battery might just solve or at least narrow down your issue.
I see you are located in NY. I had the same issue when the weather turned cold in MI this winter. Both fobs failed to start my 2018 Sahara unless pushed against the start button. I bought 4 new fob batteries, installed 1 in each of the fobs and put the other 2 in storage inside my ride. Problem solved.
I swapped the 2450 fob battery in mine as I was showing fob not in car yet it still unlocked my Jeep. I only got 1 fob with my used Rubicon, ordered a 30.00 fob off Aliexpress, 15.00 to laser cut the insert, 99.00 to program at the Dealership, works great and having a 2nd fob is way easier than dealing with no fobs later.