The Due SAM3X processor has a bootloader built into ROM memory. It can't "not have" a bootloader, or lose the bootloader. There is no "Arduino bootloader" for the chip, and you should never need to to do "burn bootloader."
It's vaguely possible that the GPNVM1 bit that selects "boot from the internal ROM bootloader" could be set wrong, but the "erase" button on a Due should override that.
It's also possible that the USB/Serial firmware could be wrong (might need a special version for Due, to handle that "erase" thing?)