When Veeam backup job is running for a SQL server VM and the "application aware processing" is activated on the job Veeam is not capable of using the VSS Writers to backup the databases. Instead, Veeam will proceed with a full backup. The disadvantage is when you need to restore backups in crash-consistent state, you won't be able to recover just the application items (databases, mailboxes, AD objects, etc...), you'll have to do a full restore or just OS files but no application objects recovers.
Notes:Veeam even has a KB article for the issue. https://www.veeam.com/kb2095
Most of the time, it looks like it's a database naming issue. If your database names contains spaces in them, Veeam is not able to use the SQL VSS Writers.
I strongly suggest that you go trough that article before trying the solution found here. However, in my case, none of the solutions worked from veeam's article.
Solution:I had to login to my SQL server and under services, change the "SQL Server VSS Writer" service logon account to a domain user account instead of "Local System" account.
Once you do this, your next backup will be processed properley with the application aware processing.