If you think that problem is with vss or snapshot free up atleast 20 % space on each of the drives being backed up . This is required for the snapshot to be created during the backup process.
I doubt this has anything to do with VSS.
First steps: if running SSR 2011, make sure the machines are running latest service pack - SP3 (version info will show 10.0.3). If running SSR 2013, make sure the machines are running latest service pack - SP1 (version info will show 11.0.1).
As above person mentioned, please confirm if this is only seen with incremental backups or both incremental and full backups.
You mention technical support - please provide the case number if you have one.