I recently bought a 6" digital caliper off eBay (about £7, probably identical to the Aldi one at a similar price or two-three times that from the usual suspects).
I just happened to find this link c/o the Wikipedia page
- which says the battery is always in use (the "off" button just turns off the display) and a regular LR44 will be drained in less than a year. That explains all those Amazon purchasers' comments that the battery was DOA.
So if you only use it rarely - which is likely if you bought a cheap Chinese one - you might want to take the battery out during storage.