Dear Linc Davis!
I have the exact same problem, hopefully you will receive my output, which is below following your commands. I can not see the drobo under Go -- Computer and i can only see its contents under Disk Utility -- right click on Drobo and Open Drobo.
I had my Drobo USB connected to Mountain Lion MBPro, changed to MBPro Retina on Maverics and went to Mac Mini Server with Maverics and after years of absolutely no problems with Drobo - its now gone missing. I am quite sure it has to do something with permissions, but do not know how to fix it.
Please help!! There is 6 years of my digital life on there 😟
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total 8
drwxrwxr-x 6 501 20 - 340 Mar 12 12:55 Clients TM Backup
drwxr-xrwx@ 29 0 0 hidden 1054 Feb 21 12:35 Drobo
com.apple.FinderInfo 32
0: FFFFEEEE-DDDD-CCCC-BBBB-AAAA00000059 allow list,search,file_inherit,directory_inherit,only_inherit
1: 73F247A6-B700-47BD-8924-190C6928D04F allow list,add_file,search,add_subdirectory,delete_child,readattr,writeattr,readextat tr,writeextattr,readsecurity,file_inherit,directory_inherit
lrwxr-xr-x 1 0 80 - 1 Mar 10 15:56 Server RAID -> /
drwxrwxr-x 6 501 20 - 340 Mar 12 12:55 Server TM Backup