I have a cheap side chair I which the arms are attached with screws.

Vibrations n a washers = problem ask a motorcycle dude or gal

Turn the chair on its side, fill the holes half way with wood glue. Re-insert screws. Let it sit overnight, do the other side.

You could try finding larger screws. Or, you could use Elmer’s wood glue (for wood arms) or Elmer’s school glue for plastic. Metal arms might require something stronger, like Girilla glue, which actually might work on any surface. (Never used it so I can’t say for sure) just use a small brush to spread the glue onto the screws then replace them in the chair. ;)

fill the screw hole with wood glue and shove a few toothpicks in the glue. After it dries saw off the part of the tooth picks sticking out then screw the screw back in. If you want to you can then cover the screw head with clear nail polish. They should stay in for a long time now.

Next time the screws fall out fill the holes with wood putty. Let it dry then put the screws in.

you could try replacing the screws with gorilla glue and dowels... go to Pinterest or Youtube to show you how to use dowels and glue to join 2 thing together..

Raul Plug and then use screw

I would put the next size fatter screw in there cause the hole has worked loose, or you can glue a wooden dowel in the hole with carpenters glue on it, hammer in with a mallet, and then rescrew the old in there.

Rubber & glue between metals to maybe a magnetic washer