I personally believe that the Digital Handsets are not fit for purpose. As soon as there is break to the service all the phones need to be totally set-up again, and again and again until eventually they connect. However they do not all connect at the same time or even on the same day!!! In the mean time you have to wait until the battery dies for the really annoying setup pinging to stop.
SORT it out BT before you end up in the coroner’s court when an emergency call fails and god forbidden a Fatality occurs.
Anyone dissatisfied with a DV handset doesn’t have to use them , if it or they were supplied for free ,remove them and simply use whatever phone you had previously , if you paid for a handset , explore returning it it them to the supplier , for a refund.
Given the thousands that must be in use & that you are the first that I've seen describe this behaviour, it would suggest that it's not the phones. Maybe you have a faulty SH2?
I certainly haven't experienced that.
Of course it won't connect if you have no broadband connection.
Your original post said that the handsets don't reconnect once service is restored.
That’s correct they wouldn’t connect after the router was remotely rebooted . This is a known fault with the Handsets.
They will not reconnect if you do a factory reset of the home hub, or have allowed the helpdesk to do a remote reset.
@Buddhagb1 Your original post made no mention of factory or remote resets, which are not necessary to restore service after a break.