Once Veeam Backup database reaches the maximum allowed size, Veeam Backup & Replication will stop functioning completely.
If you choose to host the Veeam Backup & Replication database on Microsoft SQL Server Express, be informed there is a 10 GB database size limitation for this edition. For details, see Editions and Supported Features for SQL Server.
Due to its limitations, Microsoft SQL Server Express Edition can only be used for evaluation purposes or in case of a small-scale production environment. For environments with a lot of VMs, it is necessary to install a fully functional commercial version of Microsoft SQL Server.
Do not back up to tape large number of files (over 1 000 000 files in 1 000 folders) in one tape job if your Veeam backup server uses Microsoft SQL Server Express edition. Processing a large number of files will result in considerable performance penalty. Also bear in mind that the usage of Microsoft SQL Server Express Edition is limited by the database size up to 10 Gb. If you plan to have larger databases, use other editions of Microsoft SQL Server.
The best way to resolve the issue would be to upgrade your SQL Server to a Standard or Enterprise edition or move Veeam Backup & Replication database to another SQL Server with the required edition. The procedure for configuring Veeam Backup & Replication to use a new SQL Server connection is described in the Migrate using SQL Backup section of the following KB article: KB1889: How to move the Veeam Backup & Replication or Enterprise manager to another server