I have the same Frankfort Arsenal calipers as you do and initially ran into the same problem. With a few small changes they now always work perfectly.
The dirty little secret is that these electronic calipers are sensitive to battery voltage, and most importantly, they have a small drain on the battery when not in use. You can put in a new battery and they work perfectly. Leave the battery in and not use them for a month, and they may act up the next time you go to use them. The reason is that (I measured the battery voltage with a multimeter) it drained most of the useful battery life even though not used.
The solution: Buy and install a new battery and check that they work the way they are supposed to. If you have had off-brand Chinese #357 batteries, try buying a 3-pack of Energizer batteries. It may be that the off brand Chinese batteries have a slightly lower initial voltage.
If it works well with a new battery, then remove the battery after every use and just set it on your shelf. By doing this, I get 5-6 times or more the battery life and don't have a problem with these electronic calipers by Frankfort.
If with a new battery they don't work correctly, then get a new calipers.