Found this interesting question on Cigar Aficionado:
I was smoking a cigar when the wrapper began to crack and come undone. Ultimately, the whole wrapper came off. It had been in my humidor for several weeks, and I was very disappointed. Was this a manufacturing defect or was it something else?
Cracked Cigar Wrapper
My first thought, of course, was that his humidor wasn't doing its job. Cigar Aficionado thought it was possibly for the same reason...
However, they also gave him several possible solutions to the problem which are worth considering, especially if you're spending big bucks on your smokes.
While we can't pinpoint the exact reason without knowing the full details, we can offer a few likely culprits.
The first, and our best guess, is your cigar was too dry. Either your humidor or the tobacconist's humidor was not humidified correctly, which is somewhere between 68 percent and 72 percent. Since it had been stored in your humidor for several weeks, most likely the cigar dried out during this time.
To keep your cigars from drying out, first check your hygrometer to make sure it is properly calibrated. Next, ensure your humidor closes tightly so that the internal humidity level can be maintained.
Although in all likelihood that may have been the problem, they indicated that there are a couple of other possible culprits as well.
Second, you may have inadvertently cut too much of the cap off your smoke. The cap on a premium, handmade cigar is designed to secure the wrapper. When a cigarmaker finishes the head of a cigar, he or she applies a gomma, which secures the wrapper in place. Cut too much off and you will remove the part with the gomma, and the wrapper will begin to unwind from the cigar, ruining your smoke.
The third scenario, however, is that the manufacturer could very well have not applied enough gomma to the cap atop the head of the cigar. In this case, even a proper cut can cause the wrapper to peel off.