You are correct. The Alerts by default are executed every 60 seconds and have a timeout just before the new Alert is queried again. If you are seeing a lot of these Errors you can check the database to find out which Alerts are having this issue. We log the timestamp of when the error last occurred as well.
--SQL Query to pull back the Alert Name, Description of the Alert, SQL Query used, Last Time the Alert was executed, Last Time that the Error Occurred, Error Reported.
Select AlertName, AlertDescription, TriggerQuery, LastExecuteTime, ResponseTime, LastErrorTime, LastError from AlertDefinitions where LastErrorTime is not null