After checking online with a DELL representative, and me checking with a former coworker too, we are going to try "flow control" setting, both sides: NIC level and run the command on the actual switch where the SAN is connected to.

Based on the errors, the backups (which any DBA knows are pretty read intensive) are overloading the iSCSI because too much TCP/IP traffic on that SAN, disconnecting the LUNs. The flow control may provide a way to slow down the backup traffic a bit and avoid the overload.

A 2nd alternative (suggested by our SAN guy) is getting rid, remove for good, MPIO. I am not a big fan of it and don't even know if a SQL Cluster can run without it, or if the Cluster will break after removing MPIO. But if he does, he will remove it from passive node, reconfigure all NIC and stuff setting there and then we will failover that one and test backups. I do not think this is doable though ...