Clean the battery contacts with a pencil eraser or similar, blow out residue, then use a q tip & rubbing alcohol to rub them with to finish the job.
On the batt door itself you'll see 2 oblong flat contacts near the door hinge these need to make solid contact with the 2 small pins in the body. Occasionally this contact area gets dirty, worn or pins slightly depressed, clean these also, you might try gently prying/pulling the 2 pins upward.
Without batteries inside, does the door shut firmly without much movement / play.
How old are your batteries?