My DLC isn't showing up in The Beatles: Rock Band. Why not?
First, make sure you're only purchasing The Beatles: Rock Band downloadable content. Regular Rock Band DLC (including John Lennon and Paul McCartney tracks) will not play in The Beatles: Rock Band, and vice versa. The Beatles: Rock Band is a standalone game, and will not export to any other Rock Band title as well.
If it's definitely The Beatles: Rock Band DLC you're purchasing, make sure you're downloading it to your console. Otherwise you will need to be connected to the internet to play the songs, and any loss of internet connection could cause problems.
If all else fails, delete the downloadable content files from your console or external hard drive (SD card, USB stick, etc.) and re-download from your purchase history.