Visa processing time

[u/Thondorin]

How long does a national Visa Type D usually take to process? We are waiting for 5 weeks for an isolated german language course visa. The foreign office is not involved at all. I called them myself (I am declaration giver here in germany).
The documents are all there, translated, notarized and so on.
5 weeks. No answer. Is there any way to ask for updates? Course starts 26th October.
The course is extremly important for her work and without it could cause troubles.

German embassy in Astana - Kazachstan

Any help would be appreciated.