Well, first of all, stop hooking up with guys who make you leave right after you've done the deed. Who are these d-bags who are giving you the boot and not at least letting you stay through brunch? There's nothing wrong with asking if you can sleep over. Are they literally showing you the door afterwards?

But, bigger picture: if you are just "hooking up" with these guys who can't wait for you to leave after getting off, why do you want to do something intimate like spend the night? "For the night" sounds like this is a one-time thing, and that you're talking about more of a general "guy" than just one guy who you have feelings for. Why do you want to sleep over if you're just looking for a series of one-night stand? Do you always want that awkward morning after? Are you just looking to escape your apartment? Perhaps use someone else's shower? Are you conducting a survey on silk versus cotton sheets?

First, examine why you want to sleep over. Are we talking about one guy here who you have feelings for? Or do you want to spend the night with "Joe Q. Hookupington" to see if things can progress further? Honestly, the best way to ensure that you sleep over is to just keep fooling around until you both pass out from exhaustion. He may have issues with people sleeping over, and ask you to go. (At the very least, I hope he gives you cab fare.)

If this is just "hooking up" then you should reexamine your terminology. Are you interested in getting to know this guy better? If that's the case, then you should go about establishing that. Are you looking for a place to stay because you hate your roommates? Then try to solve that problem instead of using your latest hook up to get away from your roommate who always lets her drunk friends crash on the couch.

If you feel like you're connecting with the guy, there's nothing wrong with asking if you can sleep over. If it's late, say it's a safety issue. But, really, what I think you're looking for is a relationship. Maybe it's time to cut back on the random hook-ups and start looking for someone who will be happy to see you the next morning.