Electronic – battery lifetime with self discharge

Among mainstream battery technologies, LiPo has the best energy density, so you will probably want to go this way. In your case, since you will use a regulator anyway, every configuration possible (including single cell combined with a step-up boost regulator). Once you have chosen the total energy capacity you need for your application and the cell configuration, there are two parameters to consider:

1. Quality: for the best specific energy, you will need to get high quality cells, which are going to cost more.
2. Discharge rating: cells are usually rated for a given maximum discharge current, usually expressed relatively to its capacity (for example, a 10C rating for a 1000mAh cell means that the max current is 10*1000mA = 10A). While higher C rating may mean a lower ESR, there is a trade-off and increasing C rating significantly lowers the specific energy. As an example, a 40C 2000mAh cell from a high quality chinese manufacturer I was looking at recently had a specific energy of about 140 Wh/kg while the 15C version had a specific energy of 170 Wh/kg. This difference can largely offset any loss due to slightly increased ESR.

Whatever configuration you will end up using, your require that the battery lasts at least 5h. Assuming little loss in DC-DC regulation, this means that the average current would be at most 0.2C and the peak current (from your numbers) about 0.6-1C. I would thus look for 5C-rated good-quality cells, which should get you 180Wh/kg or more.

Your solution will work in principle.

The following will work for any generic uC (microcontroller).
You could automate it by providing a high side switch (MOSFET or bipolar) that was turned on with a momentary action push button, held on by the uC, and turned off by the uC when desired. There is then no prospect of hunting or hysteresis as the battery voltage rises when deloaded as when it's off it stays off until the user turns it on.

Size R2 to suit output current.
MOSFETS can be used for Q1 or Q2 with minor changes.
Switch Go! has to be held low until the uC takes over hold-on control.
Adding a capacitor across SW1 will allow circuit to remain on for a small period until the Arduino takes over.

^{simulate this circuit – Schematic created using CircuitLab}

For extra points have a warning buzzer at a slightly higher voltage so you get a chance to take action before auto shutoff (hat tip to 46464).

The divider resistors should be as high as the ADC spec allows to minimise wasted current (only about 0.5 mA here but it all helps).

0.9V is well down the NimH discharge curve - especially if current is <= C/5, as is usually the case in this sort of application. I'd use closer to 1.0V/cell. Higher cutoff voltages will give substantially better cell cycle life with only a small decrease in available battery capacity.