Arduino watchdog with 555 Timer and a MOSFET
These microcontrollers used in Arduinos typically contain a so-called Watchdog, which fulfills exactly the role of your 555, but is 


already integrated, thus needs zero additional components (and thus, sources of failure),
uses an amount of power that is, even with lab equipment, pretty much impossible to measure, whereas the classic 555 is a true power hog, 
can be way more accurate,
will reliably reset your system exactly once until it is started again (which you typically do early on in your firmware),
is designed and tested by experts for production in the millions to billions and I'd thus expect it to be way more reliable than your own analog circuit and
leaves your Arduino in a defined state instead of violently disconnecting it from power, which leads to a brown-out situation with currents flowing in directions noone foresees.


So, abandon the 555 approach and simply learn how to use the watchdog. It's superior in any aspect I can think of.