I can't believe that in the 21st century we are unable to build a 9V battery that lasts more than a few months in a DMM.
I avoid Duracell because of their proven track record of dismal failure. So I bought a store brand alkaline 9V here in Montreal, it's the brand of a big chain pharmacy. It's usually good stuff.
This morning the DMM was dead. I took the battery out and measured with my analog meter and it's 0V. Flat line. Took the battery apart and it's 6 x 1.5V cells and they're all covered in white corrosion.
We're talking 6 months here, with very little use.
Is there a known good brand?
Of course we are able to build a 9 V battery that lasts more than a few months. My RadioShack 22-812 meters take a 9 V battery and the same battery will operate the meter for 2-3 years of intermittent use with no trouble at all.
You need to ask not about the battery, but about the meter.
What meter is it?
What is the quiescent battery drain when the meter is switched off? Have you measured it?
Does the meter have a soft power switch or a physical one? Soft or standby power off switches continue to drain the battery.
How much are you using the meter over the six months? Are you using it a lot, or is it just sitting on a shelf?
Usually, when there is excessive battery drain it is not the battery that is at fault.