Look, it sucks when the games we buy don't work as intended. It's almost worse when a game that used to work just fine actually becomes broken for one reason or another. That's been the case with Mortal Kombat lately, which was working just fine online for awhile, but now that there's DLC and "klassic" skins packs out there to purchase, things have gone way, way sideways.
The problem, apparently, lies in the classic skins that came as part of various retailer-specific pre-order packages. If you downloaded these back in April and have them on your system, every game you attempt to join will, if my experience is any indication, totally fail to stay connected. According to a post on the game's official forums, a patch is in the works to fix this issue once and for all. However, you can do your part today by simply deleting and redownloading any of those individual skins that you might have on your Xbox 360. The PlayStation 3 was also suffering from this issue, but it looks like a patch is already available there that fixes this. I assume you could also just delete the skins if you've purchased that skins pack that came out awhile back, but I haven't tried that.
I'm mostly posting this information because getting it from the official site is something of a nightmare. Even a direct link to the thread would just throw the site's age gate in your face, following by a redirect to the homepage. Super annoying! This seems like the sort of info that they'd want to blast out onto the homepage of the site and the in-game Message of the Day, since it's an issue that effectively makes the game unplayable online, and both players in a match need to have performed this fix to make it work.
So, do your part. Go redownload those skins, and while you're at it, download all of the compatibility packs for the DLC characters. Because the other incredibly frustrating part of the process is that those are optional downloads, so if the person you're playing with hasn't grabbed those packs or purchased the three available downloadable characters, you can't use the characters you've paid for! Insane, right? This one can't be laid at the feet of the developers, though. This one's an issue with Microsoft's rules regarding maximum patch sizes, I believe. Stuff like this is what makes me want the next generation of consoles to come sooner rather than later. Hopefully they'll be able to guarantee hard drives in all machines next time and force multiplayer patches down to all players to keep everyone running the same stuff at the same time.
Oh, also, Rain is available today. He's pretty crazy, I bet the combo videos will be nuts.