GSM network problem

That should indicate that the modem is registered (or, at least, that it thinks it is registered);
if it were in the WIND: 7 “stuck” state, the LED would be steady.

Indeed - the modem thinks that it is registered…

… but the network thinks that it is not registered!

If you enable delivery receipts, does the network think that the SMS has been delivered?

I mean, can you reconnect to GPRS once this has happened?

If so, does reconnecting to GPRS also restore the GSM registration?