The path discovery and mount process can take a while to populate the correct path to the VMDKs.
16.05.2012 18:28:09] <26> Info [AP] (Client) output: VixDiskLib: Trying to open disk [Datastore] VMName/VMName.vmdk using mode san.\n
[16.05.2012 18:34:41] <26> Info [AP] (Client) output: DISKLIB-LINK : Opened 'san://snapshot-16089[Datastore] VMName/VMName.vmdk@XXX?veeam02/XXX' (0x1e): plugin, 62914560 sectors / 30 GB.\n
[16.05.2012 18:37:01] <17> Info [AP] (Client) output: VixDiskLib: Trying to open disk [Datastore] VMName2/VMName2.vmdk using mode san.\n
[16.05.2012 18:43:27] <17> Info [AP] (Client) output: DISKLIB-LINK : Opened 'san://snapshot-16091[Datastore] VMName2/VMName2.vmdk@XXX?veeam02/XXX' (0x1e): plugin, 62914560 sectors / 30 GB.\n
There's several possible causes to this behavior. Some Multipathing software can cause delays in choosing the correct path and cause it to recalculate this path. Another possible cause is latancy on the C:\ (System Partition) as it's also included in the storage discovery process. If the C:\ drive is on stored on a raid controller, having it failover to write-through instead of write-back mode can cause enough disk latency to cause the same issue. This can occur in some instances such as raid controller battery failure or if the write-through mode is already set.
As this is an environmental issue, the first thing to do is try to isolate possible causes. Verify MTU sizes match, remove/disable Multipathing temporarily, check for latency on locals drive on the Veeam server or with SAN itself.