Days since last backup alerts

The Days since last backup alerts indicate the number of days that databases (per-database or at the instance level) have not been backed up.

To see more information about these alerts applied to Availability Groups, check Days since last backup for availability groups

Days since last backup at the instance-level

The Days since last backup alert applies to any database at the instance level. This alert is enabled by default.

To configure thresholds and employ alert filters such as excluding specific databases, follow these steps:

To configure an instance-level alert:

Right-click a SQL Server instance in the Servers tree.
Select Configure Alerts.
Select the Days since last backup metric in the Alert Configuration window.
Click Edit to modify default threshold (number of days).
Check the boxes next to Informational, Warning, and Critical to include alerts for these states.
Change the alert thresholds by moving the arrows to the appropriate levels or by double-clicking the value and typing a new threshold level.
Click Advanced to apply advanced settings such as alert suppression or alert filters (excluding a database from alerts).
Click OK to accept your changes.

The Days since last backup alert applies to a specific database in your monitored SQL Server instance. This alert is disabled by default.

To configure thresholds and employ alert filters such as excluding specific databases, follow these steps:

To configure a per-database alert:

Right-click a SQL Server instance in the Servers tree.
Select Configure Alerts.
Select the Days since last backup metric in the Alert Configuration window.
If the metric features a per-database, on the Configuration tab of the Alert Configuration window, click Add. Use the drop-down list to select the database to which you want to apply these settings.
Check the boxes next to Informational, Warning, and Critical to include alerts for these states.
Change the alert thresholds by moving the arrows to the appropriate levels or by double-clicking the value and typing a new threshold level.
Click Advanced to apply alert suppression.
Click OK to accept your changes.

Here are some scenarios applied to Availability Groups:

When primary and (any or all) other secondary servers are being monitored: Primary server displays the last backup date alert by checking all other secondary servers for the latest backup date of that database. If the latest backup date across that Availability Groups justifies the alert, it displays. The secondary monitored databases also display the same alert, as the latest backup date for an Availability Group across all replicas will be the same.

When only primary replica of a database is being monitored: In this scenario the alert displays after SQLDM checks the latest backup date across all replicas and if that date justifies the displayed alert.
When some secondary replica is being monitored but no primary replica: In this scenario the alert displays after SQLDM checks the latest backup date across all replicas and if that date justifies the displayed alert.

Limitations

The assumption is that the connection credentials of all the replicas are the same. At this point SQLDM stores connection credentials only of the monitored servers. If a secondary replica is not monitored, the connection credentials are unknown. This setting can not be included in the properties as a number of secondary replicas because is not limited and also its db specific.
A replica may have the latest backup date, but it is possible that the sync is broken between replicas, in which case the db would have been backed up but the some data would not be there. In this case, the alert may not come if the last back update does not justify an alert.