Based on what we know so far, I would say the root of the problem is that it is a low-quality no-name multi-tool.
Thus, my first and best suggestion is to buy, carry, and use a high quality tool. If the current tool has sentimental value, then put it somewhere you will see it often (e.g. on your desk as a paperweight).
If you are determined to continue using the tool you already have, I would probably try a very small amount of Loctite (try the blue first) on the threads of the offending screw. Make sure not to Loctite anything that is supposed to be able to move.