How can I lose my trike in Death Stranding?
Solution 1:
The first trike you get in the starting region is not owned by you, and thus cannot be repaired or stored in a garage. This means if you lose it in deep water, it's damaged my timefall, or otherwise destroyed it cannot be recovered as you will not yet have the plans to build your own.
BTs can grab your reverse trike, but it should be recoverable if you defeat or escape the BTs. If you walk more than 1000 meters away it may despawn, as would any other cargo dropped and abandoned.
With that said, it does not seem to be a part to the Chiral Network and thus doesn't seem to be accessible by other players - and shouldn't be lost if you save and log out.
You won't get the ability to construct reverse trike until you leave the starting region and complete a few missions in the next region, so keep this one in good condition if you can.