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If you happen to ping a network client during a DHCP renewal, is it supposed to respond to ping requests?

I've noticed that whenever the execution of my scheduled network checking script happens to coincide with a client's DHCP renewal, that client briefly stops responding to pings, independently of which OS it is running, causing my script to flag it as down.

My main concern is that frequent DHCP renewals will cause service interruptions for the users.