Are you using iTunes Match? Because that's mostly the nature of iTunes Match. It tries to conserve your memory by removing songs that have not been played in a while. It should get more or less aggressive about this depending on how much storage space you have available on the device.
I don't know of any way to override this behavior, other than turning Match off.
If you are not using iTunes Match, then any songs/playlists that you sync through iTunes on a computer should be permanent (until manually deleted or un-synced)
If you are not or do not want to use a computer to sync, try downloading the songs in from the Purchased tab iTunes Store app instead of the Music app. It's likely the Music app works more like iTunes Match, in that it's about playing the music now, then conserving storage space if it isn't played often. The iTunes Store on the other hand is a download this on my iPad kind of place.
Good luck.