Our Residency expired in May, and we had already applied for Long Term Residency in March (but this is taking months to come through with the new Residency Card). Our SGK was automatically cancelled when our old Blue Book residency expired by the authorities. We were told we would have to wait until we got our new Long Term Residency Card and show it to the SGK Office before it could be reinstated.
BUT, yesterday we took the letter from the Passport Police stating we can leave the Country for 15 days (this shows the start and end date of the new application - end date being 2099), and the FETHIYE SGK Office reinstated our SGK - no problem.
Hope this helps anyone in a similar position to us.