I got worried about over agressive NiMH discharge after reading the Eveready tech data page on NiMH. It includes this text:
"To prevent the potential for irreversible harm to the cell caused by cell reversal in discharge, removal of the load from the cell(s) prior to total discharge is highly recommended. The typical voltage profile for a cell carried through a total discharge involves a dual plateau voltage profile... The voltage plateaus are caused by the discharge of first the positive electrode and then the residual capacity in the negative. At the point both electrodes are reversed, substantial hydrogen gas evolution occurs, which may result in cell venting as well as irreversible structural damage to the electrodes. It should be noted that the nickel-metal hydride cell, because it uses a negative electrode that absorbs hydrogen, may actually be somewhat less susceptible to long-term damage from cell reversal than the sealed nickel-cadmium cell."
You may wish to view the passage in context. Here's the page:
http://data.energizer.com/batteryinfo/application_manuals/nickel_metal_hydride.htm
Eveready's general, probably conservative, recommendation is to avoid discharge below 0.9 volts. I wouldn't be surprised if the Infinity cutoff was around that level, and matters would get much worse if it went dead right after I snoozed off. Eveready includes a formula for batteries run in series. The more batts the higher voltage at which you should stop and recharge them.
Next time I run my Infinity dead flat I should check its remaining voltage. The good news is that NiMH cells don't have a memory effect. I suppose that the safe approach would be to pull the cell 1 or 2 nights before it is scheduled to run out.