If they sit in high humidity for too long, it can cause the natural vegetable glue that is used in cigar rolling to moisten up and cause the wrapper or cap to become loose and possibly unroll/fall off.
You can also possibly have a problem if they are at a higher humidity, I cant remember off of the top of my head what can happen other than mold chance...
Also, I think that cigars at above 72% start to taste funny.