My H10-13x must be one of the original models - The battery module holds 6 x 1.5v AA batteries (total 9 volts). They seem to go on for ever - but I would say in excess of 40 hours and maybe up to 50 hours. I should keep a record in my logbook to track the usage!
I buy a box of 40 AA Digitor Alkaline batteries from Dick Smith Electronics (about $25), with the last box lasting me well over a year.
If you are using the new model, which I understand utilises a single 9 volt (expensive) battery, the overall capacity of the battery is far less, therefore the life for one battery would also be less.
I have also purchased a David Clark accessory - a spare battery pack holder and pouch, so if it seems that the batteries are on their way out (an uncomfortable sensation) I can easily swap over in flight.
As for ANC/ENC headsets actually being harmful, I can only say that I always feel more relaxed and less tired at the end of a flight than I did when using my old H10-80's - good as the 10-80's were they just don't compare with my 10-13X's - even when used in passive mode.
Hope this helps.