Same or similar issue. Base game, latest non-beta version.
Four transports in a fleet. Population 9 in each. Moved them to a starbase to keep them out of the way and safe. About 20-30 turns and at least one save/load game cycle later, when they left the starbase (perhaps) they all had no population showing, which I discovered when I tried to use them to invade a planet.
Going to go test now if they can have any more population loaded back on them from a friendly planet.
Edit: I was able to load population back up again from a friendly planet on the transports which had lost it. It also persisted through a save/load cycle, so bug appears to be starbase related.