I'm not sure how your trainer tightens onto the skewer...it looks like both sides tighten? Are they loosening from vibration after riding a while? Is there a lockring or something else that locks the clamp in place after tightening?

If both sides tighten, then I would think you'd actually want to tighten both sides (don't just tighten one side and push it into the other side).

If you have the proper skewer ends, and the clamps are tight (and staying tight), bikes just don't fall out of trainers.