I have had the same issue this summer with my PMD670, twice. The battery went from full to empty in about 10 min just over an hour into the set. I considered that their may have been a single rechargable AA that was bad, or not charged correctly, something like that. My deck sits at 45 degrees, not flat, and not standing on it's end as you are doing. I replaced the 2500 Energizers with 2650 Duracells, and ran for Jason Isbell last week, 2 hours straight through, and the battery indicated a full charge and the end!
I don't know what to think, but I don't like dealing with the risks of being suprised by a bad cell, so I am leaning towards a DVD external. One more time with battery issues, and the AAs are outa here.