This sounds very simple and straight forward, but it a common problem. Quite oftem drill bits can have a tendancy to work themselfs free when grippen in a keyed chuck.
This is usually caused by only tightening the chuck at one point. Three Jaw chucks have 3 holes for the chuck key to locate. It is important the the chuck is tightened on all 3 holes with the chuck key. This should prevent the drill bits working their way loose.