If you think it is driver related, go to the VMware downloads page for ESXi 5.1 and see if there is a newer driver for the LSI controller that your server is using.
Also, back to your vmkwarking.log and look for the events that tell you the scsi sense code that is returned when the diconnects happen, and look up what they mean, that might give you a clue as to what is happening.
If you can predict when this is going to happen in real time, or within an hour of it happening, look at your real-time performance graphs on your host, which give you more granular detail. Look for command aborts. Also look at esxtop while the performance is bad and look over the disk and adapter views... see what your kernel latency and queuing stats are.