The timeperiods only cover alerting coverage for that particular service, as referenced by the notification_period directive in services.cfg.
To specify how often services are checked, normal_check_interval is what you need (here, we check every 2 minutes), then we retry on failure every 1 minute, and notify every 20 minutes until the service comes good or is acknowledged. We also check the service 3 times before alerting (i.e. the failure, then two retries).
Code:
define service {
...
max_check_attempts 3
normal_check_interval 2
retry_check_interval 1
notification_interval 20
notification_period mytimeperiod
...
}
Cheers
ZB