Since the H10 is warranty, it would be free, but they are backed up and it'll be there for probably several months. I don't know what it would cost to fix yours, they may not be admitting they have a problem. It would also be a board failure, perhaps the temperature sensing is faulty and shutting down the audio prematurely.
The H10 issue shows up with maximum audio, if you run at full volume, crank up the labored chuff so it's as loud as it can be, and then toot the whistle a few times, it'll usually cut out. It needs a little time to "warm up" before the thermal cutout triggers.