Available in a variety of strengths, thread-locking fluid is great at keeping screws where they need to ... on Hackaday – check out this method on removing enamel from magnet wire.

Allen screws made from weak metals strip quickly, and using the wrong size Allen wrenches/hex keys can also damage them.

If there is tremendous resistance, remove the screw entirely, then see instructions to sink the anchor into the wall. With a sharp tip and threads, threaded drywall anchors are similar to screws.