Graviteam

Several times during the battle phase I suddenly get a notification that I lost one of my mortars (while moving) even though they were not under fire. The crew seems fine. What is this caused by?

Sometimes crews can not install a mortar after moving. Yes, it happens.

And then the whole mortar is lost?

Sometimes, crew can fix it and manage to reuse it

What's the logic behind the mortar becoming unusable by just being moved?

The mortar can not be used when disassembled. The mortar is transported in disassembled state (typically in 3 packs), as a consequence it can not be used when transported.
It is also obvious if at least 1 pack is not delivered to the assembly site, for example if the one who carried it was killed on the way. The mortar will not be able to assemble and it will be unusable.

Yes, but this also happens (a lot) if the unit wasn't even under fire. Maybe a stamina thing? Like they ditch it when moving?

Sure but if I'm reading the comments correctly the game is not relating it to an event like that. It's just rolling a die and creating an abstraction.