rsync (but also other commands) run with nohup gets SIGHUP

I'm connecting from my computer to a HP UX B.11.31 system and am running some very lengthy there commands using nohup so I can go to sleep and do something else for a few days while they complete. Example of such a command:

nohup rsync --rsync-path=/usr/local/bin/rsync -e ssh /data/src usr@target:/data/ >> /data/log/sync.out 2>&1 &

Note: the Rsync command's target is a different HP UX server. It'll run and run, until my computer somehow gets disconnected from the HP UX system (it's connected through SSH over a VPN over my home connection, and disconnections seem to happen once a day). If this has happened, I can tail /data/log/sync.out and I'll find:

Killed by signal 1.
rsync error: unexplained error (code 255) at rsync.c(549) [sender=3.0.8]

Someone suggested putting the command in a shell script and running that with nohup instead. So I did that (with a shebang for #!/usr/bin/bash), and then ran the command as nohup ./auto_rsync.sh > /data/log/sync.out 2>&1 &. The same thing happened. The funny thing is that if I simply log out while the command is running by typing exit, the command will keep running. So why is only my disconnect sending SIGHUPs to a process running with nohup?