I lost a bunch of squash and melon seedlings as well. I put a cage around them, but that didn't help. From that I sorta concluded that it was probably a flying insect. So I put a sheet of Agribon (row cover) over the cage and just buried the edges with soil so it was completely enclosed.
After two weeks of that, they'd grown large enough that I could take the Agribon off, and now they just grow faster than the bugs can eat 'em.