I "believe" the issue is the size of the Drobo, as you stated once you had changed the 3TB partition and used the full Drobo size the Time Machine failed. The Time machine saw more Drobo Volume that it could back up.
One of the issues is that the Drobo can not dynamically expand the Disk Size as you add bigger disk, I have mine set to 16TB but I only have 8TB (2TB X 4, of 5.42TB usable) of actual disks, the finder show 16TB, is false.