Well, thinks have improved.
I installed the latest Armbian Debian Jessie Server release and after applying all of the updates, I ended up with a more stable system.
I did still have some startup issues, so I found that changing the disp_mode parm from 720p60 to 480p or 480i in /boot/armbianEnv.txt fixes my startup issues.
I left the default setting for dhcp in /etc/networking/interfaces.
I also have another system running Armbian Ubuntu Server with Mate installed. This was also having startup issues without a static IP set.
Now, after the recent updates which I applied today, this system works with dhcp and the disp_mode parm of 720p60 or 1080p60.
These are running on a Pine64+ 2Gb.