Backing up a RAID experiencing I/O issues

I recently began working for a company that has an OS X Server with a PROMISE Pegasus Thunderbolt RAID (RAID 5) attached as a file server. Within my first couple of days, it became apparent that users were having performance issues reading from and writing to the file server (which had been a problem for several months before I started.)

After a quick investigation, the RAID was near capacity (4.99 of 5TB used, 14GB free.) We decided to purchase an additional RAID system and are expecting it within the next two days.

Meanwhile, I have been unable to successfully back up the data files. I have tried using Disk Utility to create disk images of the entire volume, as well as images of individual folders within the volume. It never completes and returns a generic error:

"Unable to create [folder].dmg. (Input/output error)."

Console shows hundreds of the following error:

kernel: disk3s2: I/O error. 

I ran "diskutil -list" in Terminal and confirmed that disk3s2 is the RAID volume. I have also tried to manually copy (or even drag and drop) important folders to another volume, but that has also been unsuccessful.

Does anyone have any other ideas that may help? This data is mission critical, so any and all advice is welcome.

Thanks in advance!