I'm with Dan on this one...

Although it could be the battery, the ignition module may not be happy. I had a similar experience with a ZDZ-50, chased all the "usual" ideas and it turned out to be the ignition module on it's way out. One of the ways that electronic components will fail is with a little heat, i.e. running it for a bit then it won't start. Let it sit for awhile and things cool off then it works again. That is exactly what my 50 was doing and a new ignition module cured it.

That may not be your problem, but it sure sounds like it's a good possibility, especially if you've verified that the battery is not the cause.