What typically should the life be of a rechargeable battery be once on the trail?
That's a loaded question full of variables including but not limited to:
1) The power consumption of the device or more accurately the rate of discharge of the cell.
2) The state of charge of the cells. Not all chargers always deliver a full charge.
3) The age and condition of the cells.
4) The temperature of the cells.
5) The capacity of the cells.
6) The time span since the cells were charged. One downside of NiMH cells is their relatively high self discharge rate. The newer LSD (Low Self Discharge) cells keep their charge longer at the cost of some capacity.
For environmental reasons I prefer rechargables. My Garmin Vista HCx will run 11+ hours on two fully charged, conditioned, 2000 mAh Sanyo Eneloop AA cells above 40 degrees F. But YMMV. A lot.
One more small but important point. Some of the newer headlamps with advanced electronics sip power even when switched off. Remove the cells or interrupt the circuit with a piece of plastic when storing.