To test it, I unplugged my Fios router and left the power live on the pap2. When I re-established Internet connectivity, the PAp2 registered right away.
FYI - the GS will re-register under that condition as well. If WAN is lost, it will re-register upon re-connection automatically. It's the lost registration without a change in WAN status where it sometimes does not re-register.
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