SlimD
Sounds like a tunneling problem. Your cigars may be too wet, causing the wrapper not to stay lit.
Make sure your hygrometers are calibrated correctly.
What RH are you stroring your cigars?
Did you buy them from a local shop or from an internet site?
How long have they been in your humi?
You may want to ash every 1/2 to 3/4 inches or so and purge when you do ash, this helps the burn correct itself and may stop the tunneling before it becomes a problem. You can purge with or without a lighter.
I assume you are lighting the cigar correctly b/c you say the wrapper burns right from the start and then goes out....incorrect lighting can lead to burn problems also...maybe, maybe not in your case.
Hope this helps.
This does happen to me also, I just touch-up and purge every so often no big deal unless it happens to EVERY cigar.