I unhooked the +5v connection between the Seeeduino and my protoboard to measure the power consumption of my external stuff. I was close - it measured 147ma. When I hooked it back up and powered it up again (its running on USB power) the pin13 LED was no longer rapidly flashing but in the slow blink of a new board.
This sounds a lot like the "amnesia" problems seen in the optiboot bootloader on Uno, caused by not initializing the "known zero" register (R1) before using it to clear the watchdog timer (as a result, watchdog timeouts occur when they shouldn't, or don't occur when they should, preventing the bootloader from starting the user sketch.)
But as far as I know, the 1280 and 2650 use an entirely different bootloader that shouldn't have this problem. (are you using the standard bootloader? You probably want to omit any "-nostartfiles" switch from your link command if you're building your own; the minimum bootloader size on 1280 is big enough that this shouldn't be needed, and it is what prevents the registers from being properly initialized.)
I'm not quite sure how to suck the bootloader out of the chip to confirm...
http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1293529218/37#37