i’m not certain if it’s valid for usb thumbdrives but there is a setting that you can place in config.txt to give the usb ports their maximum current (1200 instead of 600 i think it was) the setting is the following : max_usb_current=1
i had some problems with harddisk (not thumbdrives) that did not get enough power to boot up or stay booted up that setting “can” help. Also a good power supply is especially needed.
on side note i’m currently using my old ps3 phat 80 drive in an enclosure with my pi and that setting is not needed with this drive it was with 2 other drives i tried.
not sure if it would make a diffrence though but you could try it once.
Also watch out if you overclock and enable that setting it might be your pi becomes unstable while it was not before without that setting. Have read some issues about this but could be it’s a powering problem as well then.