It sounds like the screw hole is possibly stripped. Remove the handle and screws and examine the holes in the door to confirm.
Kind of figured that but how do you repair? Is there a recommended filler? Thank you!
I guess it would depend on how severely the hole is stripped. There are honestly a lot of solutions. Fixing a stripped out hole isn't an exact science. I have personally used a broken toothpick and Elmer's glue to help fill in a hole in a wood frame like this, but there's no saying if that will work for you in this instance. I would check with a local hardware store, they may have a couple suggestions, as well.