I made a custom board with 2 ATSAMD10D13AM parts. The are 8k flash/4k sram Cortex-M0 24QFN parts. When I power the board the IC's start but then freeze (I have LED's blinking that go solid). When I attach the debugger and start debugging, it runs fine. The debugger senses power and does not supply it. The code is modified reference design code for the Xplained Mini, it uses the same part except 16k flash. I am pretty sure I changed the part everywhere. I think maybe the ramp isn't perfect. It is supposed to be 25us or greater from 0 to 2.5V. I will measure it with a scope. Otherwise what could it be?
I had this same problem on an ATSAM4LS2A. Did you check that the watchdog is disabled from the fuses? This was my problem, i didn't have any wtd_reset in my code because i hadn't activated the wtd from the program, but it was on by default.
I haven't seen answers to my earlier questions yet, but as I'm about to go offline, I'll add my hypothesis (which might become more or less likely, depending on the answers to those questions), in case it helps.
I have seen symptoms similar to yours a few times, due to missing or insufficient power decoupling near the MCUs, or an unstable power supply. For either of those cases, the result is unstable power to the MCU(s) in a "normal" configuration (i.e. without a debugger attached). That could explain the "freezing".
JTAG debuggers will often contain a capacitor connected between the target power rail and ground pins. When the debugger is physically attached to the target system, even when the debugger is not actually in-use, it adds that "hidden" internal capacitor across the target system's power rail. Therefore in some cases, if the target is suffering from inadequate power decoupling, or needs extra capacitance due to an unstable power input, then "bingo!" the target system works - just by attaching the debugger :-)