Unfortunately Stardew Valley on iOS doesn't save your game progress if you uninstall SDV, the folder containing that information is removed. I tested this on a Day 3 save for fun (my 'fun' is weird fun) and yes, the save was all gonesies when I reinstalled SDV. And also unfortunately it's not synced to Game Center, but if you have your iThing backing up to iCloud, then that save data could still be located there.