Check the handle mechanism for proper function- when you pull the handle, does the inside catch move? Or is the entire handle assembly loose and/or becomming detached from the glove box door? If the handle assembly is loose, tighten as necessary to restore proper function. If the handle is not functioning, you may be able to remove it, and replace it with a new/used one. If the handle cannot be removed, the entire glove box door may be able to be replaced.
But check the obvious- is something blocking the latch? Or is there just too much stuff in the glove box?