Start by testing your Burly with just a single drive. Test each bay with that single known good drive.
Then test with each of the other drives, one at a time.
Yes, it is possible that a bad port multiplier board can cause something like this. The port multiplier board is inside the Burly where the eSATA cable connects to on the outside and has 5 drive connections on the inside. Only way to know if that is the actual problem is to test with one drive at a time, then test with each of the drives, one at a time and see if a drive is causing the problem.
For me to actually know what to say other than the above, you would have to tell me how the drives are formatted, in RAID, individually, more than one RAID? And when things dismount, what does Disk Utility see before and after the dismount?
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