Welcome to the Wefugees Community and thank you for reaching out to us.
I agree with my colleague Saskia. Many immigration offices (Ausländerbehörden) are short of staff and are very difficult to reach in these days. It is very important that you book the appointment for the extension early enough and that you can prove that you took care of the matter way ahead the expiration date. You may also contact the Ausländerbehörde via email and even send them reminders. This will formally prove your effort and you did all you can for the time being. I would advise you to carry a print-out of the appointment confirmation with you in case you are asked to prove your identity in everyday life.
All the best,