And this is why units like the H4n are so chea... I mean, inexpensive. Besides the crappy mic preamps they will eat batteries like a shark going through a school of tuna.
At least Tascam has the option of battery packs, and, as IDOM mentioned:
one of the reasons I prefer the tascam dr-100 - it has a small internal rechargeable battery that will kick in when the main batteries die and allow it to finish writing out the file.
Please remember that the H4n, DR-40, DR-100 and other low budget mixers/recorders are
consumer products; they are not meant for professional use, and you are trying to use your H4n as a professional product - a role for which it is unsuited. I mean, come on, what did you expect for $200. The Sound Devices 702, also a two channel audio recorder, is over $2,000; but the preamps are incredibly clear and quiet, it is built like a frigging tank, it has comprehensive routing capabilities - and the batteries last a long, long time.
Oh, and lets' do a little math...
If you buy in bulk, decent AA batteries cost about 60¢ each. You said you use 6 pairs a day. 12 x 60¢ = $7.20. If you shoot 100 days each year that's $720 per year for batteries! Okay, maybe your shooting 10 days a year; that's still $72 each year. Oh, Eneloop Batteries will set you back about $2.00 per battery plus the charger, and you will have more details to "worry" about when you shoot; making sure that all of your batteries have been charged prior to the shoot, and that you have someplace to plug in the charger when on-set. If you forget you are back to buying regular AA batteries.
This is what I mean about carefully researching your equipment purchase choices. I and others here on IndieTalk have been writing for several years now about how quickly these budget audio recorders drain their batteries when supplying phantom power, and it's been a common topic on other film and audio forums as well. Yup, the H4n is very affordable and was quite popular for a while, but only because it was the only ultra-low budget audio recorder on the market. Now there are lots of (IMO) better options out there.