There may be a small insert location that is either broken off on the cartridge, or the bonnet nut is just not tight enough. Sounds like its a two handle faucet, if I had to guess I'd say it was a Chicago style faucet. Some faucets use a cartridge thats only held in by compression. It can turn past, it the bonnet is not adjusted properly.
If its a fairly new plastic faucet, it may only be that the cartridge can be replaced and solve your problem. If you can find a manufacturers name, I could tell you exactly whats wrong with the faucet. But because there are more than 1000 different brands and styles its sometimes hard to give a complete answer.