Depends on the failure mode. Usually with flash a block has failed error recovery so can no longer be read. Since the FAT filesystem is not journalled it might be the case that most of your data is there but the drive is not mountable because metadata is corrupted. Try:
ddrescue /dev/sdd1 /tmp/mylateflash /tmp/rescue.log
but replace sdd1 with your actual device name. See if you can read any raw blocks from the drive. There are tools available (mostly on Windows) for examining and fixing a raw FAT image. You may need to install ddrescue if it isn't installed automatically by your distro.
If you can't read anything I don't know of any tricks to revive a flash drive. I once recovered data from a hard drive that was failing when it warmed up by putting it in the freezer, but I doubt that flash drives have the same failure modes.