I have seen some threads indicating that some digital measuring instruments are picky about batteries.
A Starrett 734 will play dead with a brand new battery, unless it is a particular brand:
http://www.practicalmachinist.com/vb/showthread.php/starrett-aint-used-73348p3.html
In that particular case, though, I think it had to do with the variations in physical dimensions affecting electrical contact, rather than the electrical characteristics.
Depending on the design, an instrument may draw too much current and use up the battery, or it may cease to function due to the voltage drop far before the batteries rated capacity. Also, measuring instruments are frequently incremental devices and continuously read the position so they can tell if they have been moved so you don't have to reset zero every time they are turned on. So, they are always working whether the display is on or off so they need to be very frugal with power or they will eat batteries.
Different batteries have different initial voltages and different discharge curves.
"L" series manganese dioxide batteries are a poor substitute for an "S" series silver oxide battery. The L voltage starts lower and drops off faster. And some of the no-name batteries can be poor quality.
Old batteries may be half dead when you install them. Buying in bulk (more than you need over the next 6 months) may not be a good idea.
Dirty hands when changing the battery could have an impact due to slight electrical conductivity. Also, it is not unusual for batteries to have electrical contact problems. Taking the "dead" battery out and putting the same battery back in may fix the problem in some instances. This tends to be less of an issue with coin cells, but dirty hands could again be a problem.
That said, I don't worry about the cleanlyness of my hands when changing caliper battery unless they are obviously dirty and I get >1yr life.
If you have a digital multimeter, measure the voltage before you install the battery and when you replace it. The Energizer 357 I installed in my chinese caliper a week ago measured 1.570V today and the one I removed 1.044V. A 5.0000V (4.9997V when tested) reference measured 4.97V. Measure the current the instrument draws, if you can, but this can be tricky.
If you have an SPC cable connected, the micrometer may be using power up to drive the cable capacitance and circuitry on the other end, even when off.
http://www.davehylands.com/Machinist/Caliper-Batteries/
As an aside, that page also talks about the accuracy of the cheap chinese calipers. However, only a 1" gage was used. Accuracy is slightly lower over 100mm (metric) and 4" (inches). And no temperature tests were done, etc. But the results across a dozen or so units were consistent with published accuracy.
