Grafana alerts fail to query multiple datasources

Hello,
We have grafana 8.5.27 installed and a dashboard that has a panel that displays data coming from 3 different datasources (thanos queriers). Dashboard works fine and displays a correct data, but we have a problem with alerting. When we create an alert with one or multiple queries coming from the same datasource, it works fine. But if we add a query which works with one more datasource, grafana starts displaying an error:

Failed to evaluate queries and expressions: failed to execute conditions: failed to execute query C: client_error: client error: 403

Queries to each datasource work well in the alert separately, but when alert contains queries to multiple datasources, the error appears.