Mode toggling circuit using only transistors, resistors, and capacitors?
You might be surprised how little current modern micro-controllers can draw when programmed appropriately (switching itself off most of the time), think of 1 uA or less.

My first idea would be to use a relay switch in series with the power of a micro-controller, with your switch in parallel with the relay switch. The relay can probably be replaced with a mosfet. The state can be stored in internal eeprom memory (if the uC has this), or maybe in flash (self-programming). 

My beloved LPC810 has a few bytes of RAM that are preserved in the deepest power down modes. If you switch starts the LPC810 it can switch itself to deep power down mode (typ. 220 nA).