There will be times when you cannot get access to the Rock Band songs that you downloaded for your XBox 360. Here are some steps to take to get to them again.
First, of course, make sure that the system you are using is the one you downloaded the songs onto, and that you're logged in with the right user account. Downloadable songs are often tied to a machine and user. Rock Band doesn't let you duplicate them onto multiple memory cards and hand them out to all your friends to play.
If you're sure you're on the right machine and have the right user account, the first thing to do is make sure your XBox Live account is fully up to date. You can't get access to live-related activities without being fully current with your Live account. So go out to the main XBox dashboard and log into your Live account manually. If any updates or terms-of-service alerts come up, go through all of those. Most of the time this will then fix your access to your downloaded songs.
The next thing to try is to check for any corruption in the downloaded songs files. Be careful when you do this activity. You don't want to actually delete any songs that you should have access to! This part is best done with a support tech online so they can walk you through the exact version of the game you have, the exact version of the XBox Live software, and how to check the memory files for issues. There's a wealth of things which could go wrong so it's iffy to try a "quick fix" here. Make sure you have someone who knows the exact combination you're using so you can work through it.
The vast majority of the time, though, it's simply a matter of making sure your Live account is fully up to date. Make sure you go through and validate that before you worry too much. Usually it's just a quick download of an update file, coupled with an acceptance of a new Terms of Service, and you're all set to go again.
Come by the forums if you hit a particular glitch, and we'll lend a hand with ideas! Good luck, and have fun with Rock Band!