I've had this problem on my board with everything from the screw in t-nuts, pinning screws and screw-ons (which use Core's recommended size; M5 50mm from memory?). I put it down to the plywood compressing and the changing conditions (moisture?) from Summer to Winter affecting the wood. These were all smashed in without adequate care using an 18v impact driver.
If you really don't want them to move then get some gorilla glue on them. You won't get them back of again though in one piece though I don't think.
Interesting, although most holds will need more than 1 screw, so it would need to be supplemented with drilling additional holes in the hold. On plastic holds this might be a bit of a bodge.
If you're feeling lazy then ramming a couple of 5mm screws down the bolt hole also works for most small to medium holds. Adding a pin screw helps stop any spinning. Not recommended for larger holds though, especially jugs. The extra leverage means you can rip holds off the board pretty easily.
...and won't have any jugs...
As the birch tends to come from Russia it hasn't been easy to get hold of.