Microcontroller soft off circuit not working - why?
+5V with respect to GND is not high enough to turn on Q1, which is an N-channel MOSFET in the original schematic.  The O.P. was thinking in the right direction, when he had looked-up the VGS.  But with respect to what is the VGS taken?  It's not taken with respect to GND.  It's taken with respect to MOSFET's source is at +7.5V (or some such voltage required for the 7805).  So, the if you drive the gate to +5V, then VGS &lt; 0.  It's negative.  The N-channel MOSFET doesn't stay on, because it doesn't turn on in in the first place.

A high-side switch like this is usually done with a P-channel MOSFET and a second small transistor to control its gate.  Like so:



(I didn't redraw all of the original circuit, but this should be enough to get the idea across.)