Server 2: - The one with the problem
-2gb memory
-1 cpu
-mainnet
-prune to 8gb
I figure if bitcoind ran out of memory or hit some major issue, it would log in debug.log, but there's nothing to suggest the cause of it dying.
It's an out of memory crash. 2 GB is not enough to support Bitcoin Core on mainnet. In fact, I don't think any of the normal memory reduction methods will work, but you can try them anyways. Add (or change) the following to your bitcoin.conf
dbcache=100
maxmempool=100
Also, I think the 1 core (I assume 1 CPU = 1 core) may be causing some issues as that does not seem like enough power to keep Bitcoin Core running.