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At 3.75v (7.5V for assumed 2 cell)...It appears to be a very dangerous curve. If this curve holds true, coupled with the higher current draw on the output of the regulator, the additional demand could have pulled the voltage down causing exactly what happened (again assuming that the engine then Rx failure theory is an indicator of a dead battery)...
Right, you really don't want to start a flight when your average cell voltage is at that point. One thing you have to realize about the way linear regulators work: They function as regulators as long as the input voltage is at or above the sum of the regulator's dropout voltage and the output voltage setting. Once the input voltage drops below that value, the output voltage follows the input voltage minus the dropout voltage.
Both the Jaccio and Tech-Aero regulators use very low dropout voltage regulator chips (about 0.2V), not sure about the others out there. So if the regulator was set to 6V and the battery voltage had dropped to 6V (ignoring voltage drop along the wire for a moment), the output would be 5.8V and so forth. This will vary a little depending on the current load, but not very significantly. That equates to either of them being able to give you a better survivability opportunity as the battery gets really low as compared to a cheaper designed regulator with a higher dropout voltage. However the bottom line is, once the battery gets below a certain point, nothing will save you (except a 2nd battery and regulator).
You've got to know what's left in your batteries before flight by tracking their discharge characteristics in the model you fly, the way you typically fly. Then measure before each flight and stop to recharge well ahead of the danger point. I generally don't go below 7.6V for a 2 cell pack (no load). I hate it when I hear about someone losing a model this way and I sure don't want to have a similar story of my own one day.