I have two VMs exhibiting the same errors.
Extract from dsmerror.log follows:

08/15/2017 19:37:26 ANS9365E VMware vStorage API error for virtual machine 
'fmc-edge'.
   TSM function name : VixDiskLib_Read
   TSM file          : vmvddksdk.cpp (2930)
   API return code   : 14009
   API error message : The server refused connection
08/15/2017 19:37:26 ANS0361I DIAG: VmReadVDDK(): Read failed: vddksdkRead() 
rc=-1, startSector=38871040, numSectorsToRead=8192
08/15/2017 19:37:26 ANS0361I DIAG: VmReadVDDK(): retrying vddk write operation 
for up to 120 seconds.

These repeat until the backup fails after 12 retries.
Our vmware admin says he doesn't see anything.
Is there a place I can look further, or have him check?

Google results were that it was an indication of tsm server overload, so reduce 
the number of parallel sessions.
Tried that with no change.

All other VMs backup normally.