No it is not property of any partition, it is global flag. Also it can only be set via flasher over usb (i.e. not possible from device itself). You can still boot internal flash and fix mmc from the device or fix it with linux computer and card reader if you know what is broken. Or one can just backup data and start from scratch. Also if you use ext2, e2fsck might fix something.

How does your endless reboot loop look like i.e. when exactly it reboots and what is on the display?