Today I asked the question, "What's so magic about the number 838 hrs 59 minutes?". It appeared to be the upper limit for a sum in an open source package that we use internally.
The answer came from Ben Barefield, whose search netted that this is upper range for a TIME field in MySQL. It appears that this software does the sum calculation into a TIME field and maxes out at 838:59.
Looks like that program could have used some more testing. Since it's open source, we can fix it. That's good.