Generate Alert/Email when service does not go warning

Going to throw this one out there for some suggestions. We use nagios along with a device the converts contact closure to an SNMP Trap. We use this to monitor our generators at our various sites. One of the things we monitor is when the generator performs it’s weekly test. This service called, Generator Test, is normally in the OK state. When the generator starts it trips the contact closure, which generates a trap, which causes the service to go to warning. I have email alerts disabled for this service because I don’t want to get a warning and restore email for each one of our 10+ generators. So, the question is would it be possible to send an email based on the criteria that the Generator Test service DOES NOT get to the warning state at a particular day and time? Or any other suggestions to determine if the generator test failed.

Thanks.

an extra check with a timeperiod?