How do I make a default on circuit the can latch off until a interrupt goes low?
This circuit should do what you want:



IC2 represents your RTC module; I just picked one with an IRQ output.

When the IRQ line goes low, the latch (IC1) is set (pin 3 high).  Pin 6 is then low, which turns on the P-channel MOSFET nd supplies power to the main circuit.

When the Arduino sets its output low, the latch will reset, and the power will be turned off.

(Note: I didn't include the decoupling caps on each of the IC's, they should have 100 nF caps between Vcc and ground.)