Please make sure you have the following VMware patches installed if you are experiencing this issue. These patches were released in August 2016 and address one of the more common issues that cause this failure. I notice a lot of people above are using builds that are prior to these patches:https://kb.vmware.com/selfservice/micro ... Id=2144799
Note that if restarting the management agents resolve the error you can be almost certain that the issue is not caused by Veeam and thus having tickets open with VMware is also highly recommended if you want to see the issue resolved. In many of these cases you can correlate the times of the failures to errors in the logs on the VMware hosts.
A VDDK error 1 is basically a generic error that Veeam requested a disk block from the VDDK API (also a VMware component) and it was unable to be retrieved. If your backups are running in network/NBD mode, you can be almost sure that you'll see a corresponding error on the host, one of the more common is an out of memory error. Restarting the agents simply frees memory and allows new memory to be allocated. It's certainly possible that the issues could be caused by other problems, corrupted VMDK for example, but obviously restarting management agents wouldn't fix that issue, so if restarting the management agents is the fix, then you need to figure out what's going wrong with the management agents.
Of course I'm not suggesting you can't open a ticket with Veeam, but if you do, be prepared to push the issue to completion. I looked at a number of the cases in this thread and most closed with "No response from customers", many of them did not even upload logs. These types of issues are difficult to resolve because, in many cases, once the issue is resolved, the person opening the ticket loses motivation to pursue the root cause. This is especially true if the root cause is outside of Veeam so requires opening a ticket and working with VMware as well, however, that's likely the only way to find the root cause.
There are also many other possible causes for the error, but the agent issue is probably the most common I have seen.