I've had my 1608 for about 3yrs and use an iPad 2. If you hadn't seen the exact same issue on a second IPad, I would have suggested troubleshooting the iPad. Eg. Does the iPad reboot while running MF via a wireless connection. This is obviously irelevent.
Having followed this and other boards for quite a while, I can say this is a new (or at least very uncommon) issue. The 1604 would seem to be at fault. If you got it from a store that still sells them, go in and ask to dock your iPad in their unit. Most reputable stores will be happy to help you troubleshoot. If it runs fine for an hour etc, then you've prob confirmed the hardware issue of your own unit. Depending on warranty get it replaced or repaired.
Sorry to hear about that.