Hello,
There is a feature called Alarm Level Configuration in the Alarm Settings that allows you to create rules which can change the severity of alarms after either a specific amount of Repetitions or Duration. Repetitions won't work for the "does not respond to ping packets" alarm, as it is generated only once after the first missed ping, and repeated failing pings only extend the duration of the same event (though it would be useful for alarms generated repeatedly from Traps). Duration could work here though.
For that you would first change the severity of the alarm via Trap Management > Trap Definition - search for OID 1.3.6.1.4.1.25506.4.1.1.2.0.1 or "poll packet" name to find it - to any severity lower than Critical. Then create an Alarm Level Configuration rule for that alarm (Selected Alarms) and add a Configuration Item for Alarm Duration.
For example add Alarm Duration of 5 (minutes) with level Critical - then iMC will change the severity of this alarm to critical 5 minutes after it appears. It wouldn't trigger if the device becomes reachable in the meantime, since that particular alarm automatically recovers itself.
Perhaps another alternative would be to set a longer ICMP polling interval in IMC, via Device Details > Configure > Modify Poll Interval > change the "Status Poll Interval". However you can't really know when the next status poll will be, so if it happens 10 seconds after your device goes down for a reboot, you'd still get an alarm.