Make sure you don't have snapshot autodelete turn on for the FlexVol(s) for which the DBs exists. This is a default setting when making SAN FlexVols with System Manager and is intended to keep the LUN online instead of having the LUN go offline when the space fills up. Try to also look in the storage system logs (/etc/log/messages) around the time the backups are taken to see if the snapshot was autodeleted. If that is the case, then that is your resultant cause, but the actual cause is that you have undersized your FlexVol for the amount of change that occurs within the LUN. The only solution will be to increase the size of the FlexVol.
Just this morning we had the same error. There are no other errors, OS/NetApp/SQL, that happened at the same time. First time with this error since we started using snaps. Roughly 40days of hourly backups/verifies. We are verifying on a remote SQL Server.
For us this was with SnapDrive 6.4.1 and SMSQL 6.0.0. Windows 2003, SQL Server 2008 R2 on both servers.
"waht is happening in the VERIFY DATABASE AFTER BACKUP Phase... I guess that we have some size problems on the C: cause the TLogs are too big to mount and do the DBCheck"
As I understand it, what happens is that snapshot you just took gets mounted to (in your case) C:\Program Files\NetApp\SnapManager for SQL Server\SnapMgrMountPoint\MPDisk006. This does not consume any space except perhaps for some metadata, on your C: drive. The databases which you selected to be backed up / verified are attached, DBCC CHECDB ran against them, then unmounted. This is done one at a time until all the databases are checked, then the snapshot is unmounted.
If you look in SMSQL under Reports->Backup you will find the log which is very detailed. Reading these logs shed the most light on what SMSQL/SnapDrive is actually doing.