Is it a design limitation of the SAM3X architecture ?
Yes, chapter 17.4 of the ATSAM3X8E datasheet says:
After a Processor Reset, the value of WDV is 0xFFF, corresponding to the maximum value of
the counter with the external reset generation enabled (field WDRSTEN at 1 after a Backup
Reset). This means that a default Watchdog is running at reset, i.e., at power-up. The user must
either disable it (by setting the WDDIS bit in WDT_MR) if he does not expect to use it or must
reprogram it to meet the maximum Watchdog period the application requires.
The Watchdog Mode Register (WDT_MR) can be written only once. Only a processor reset
resets it. Writing the WDT_MR register reloads the timer with the newly programmed mode
parameters.
Its always a good thing reading the datasheets of the controllers (even when you understand only 5%). but you might get an idea, what the controller is able to.