I just recovered from these same events that showed up in a client's vSphere 5.5 environment. Every second for hours on end, those "lost access to volume" events would show on all hosts. The datastores themselves never went offline, VMs never showed inaccessible, and no events showed in the NetApp logs or UCS logs related to dropping connections. VMs would also experience the issues you described. I first noticed that the Snapshots Veeam created were not getting deleted. Some had grown fairly large, one up to 31 GB and was over a month old, others smaller and newer, but still several GB. Manually deleting these Snapshots restored those VMs for a bit, but many Veeam jobs weren't deleting the Snapshots.
Long story short, I learned ESXi 5.5 was not supported with the version of code running on the NetApp, 8.1.2. I downgraded to ESXi 5.1 and all the above problems went away immediately. Veeam Snapshots were getting deleted after backup jobs just as they were supposed to, VM performance was like never before (they'd been running this way for several months), and those datastore errors never returned.
Check for incompatibilities. You might be surprised.
Cheers,
Mike