In addition to the comments about using a blue thread locker (or red if you plan to never remove them), I would wonder if a different material of machine screw might have more friction in the threads as well. Stainless steel may have had threads cut too smooth to provide enough grip. Additionally, if it is a flathead or philips type screw head you will not be able to put much force on it, even with both hands turning a screwdriver. Using a hex head or star head with a ratchet can get magnitudes more torque, just don't strip the threads.
PS: I now realized with the idea that stripping the screw from overtightening could happen on a new screw could still apply to the old screw. If you've really tightened it with all you've got its likely that the threads have been pulled out and your screws are now more like toothpicks.