One likely culprit is polyfuse F3. A polyfuse provides a small resistance, and if you exceed its rated current it heats up and the resistance increases, which causes the RasPi 5V (measured between TP1 and TP2) to drop low enough for it to fail. When you turn off power, the polyfuse cools and slowly returns to something near its original state. It may be that one board has an iffy polyfuse and its resistance is now too high.
See the RasPi Troubleshooting Wiki to see whether that's your problem. If it is, you can replace F3 with a polyfuse or a single-blow fuse, which has lower resistance. You can also just bridge across it with a wire, but that loses F3's protection. Any board modification voids the warranty, so be careful.
Another possibility is a bad solder joint or PC board trace which fails when the board heats up. These are not usually repairable, so it's better to return the board if it's still under warranty.
This seems to be a rather common complaint recently.
See for example:
In the first thread above, Liz wrote:
by liz » Fri Nov 23, 2012 1:54 pm
"I wonder if there was a small crystal batch that was faulty - (this is ONLY me wondering; we don't have any data on that). We have noticed what you've been saying here and have asked RS to let us know what they find when these boards are returned."
and James on Nov 22 wrote:
"Short answer, you need to RMA you device if you think it is faulty."
Whatever the problem is, it appears to affect boards made in China,
both by RS and by Element14.
Is there any focused effort at Element14 to find the cause of these
similar problem reports? Liz mentioned asking RS for information,
but didn't mention E14. It sounds like Liz is relying on RS and/or E14
for analysis of the problem.
Is there some commonality in the China manufacturing process that
might cause similar failures from both E14 and RS? Are they made in
the same factory? Do they use the same batches of parts? Are they
tested the same way?
I have the same issue, I ordered mine early dec 2012. Now my 2 PIs do not last more than 4 mins in text mode. I tried several SD cards, power supplies. Checked the syslog nothing shows up, even used the console option without any peripheral (keyboard, mouse issue, monitor). My kids are disapointed, I plan to return them to mcm electronics.
RPI spec: model B, box from element14, (c) 2011.12
Have you been able to find any information about the cause of this problem,
or which batches were affected?
There is a report from Element14's affiliate MCM Electronics today saying:
"A few batches ago, we had a few problems, but haven't heard of any reported recently."
in this thread: