Time to get German Invitation Letters?

It's been two years since my application for a German visa was denied. This year, I plan to apply again, but this time with an invitation/obligation letter from my brother, who has a well-paying job in Bonn. He sent all the required documents to the designated institution in his city two weeks ago but hasn't received any response yet. My brother inquired with one of his friends, who mentioned that he sent all the required documents to the designated institution six months ago and still hasn't received a response. Does it usually take this long to obtain an invitation letter?