I have 4 brand new DVMs and one uses a battery pack up in 3 days flat, turned OFF! I did some net searching and found a forum where it was discovered that Fluke put a cheap Toshiba supercap in the meter with a less than 2 year lifespan and AT the same voltage they were charging it to and everyone was seeing leaking.
I knew right away that was the cause of my problem. So I bought a higher voltage, bigger supercap with nearly the same footprint and a slightly higher profile, and stuck it in the BAD METER! and fixed that pup. It takes minimal GRINDING (yes, I said grinding) to make it clear, but it will last for years without leaking since it has a higher voltage rating and the meter will hold the date longer if the batteries do die down. They have been in it for two weeks and no depletion, so that nailed the problem.
I photo-documented the whole process in case anyone else has a Fluke DVM that eats batteries for breakfast like they are going out of style. I would have made a video, but this works. Feel free to critique or make good use of as you wish.