How long does it take to earn a 7th dan in aikido?

There is no specific time. Aikido is self paced and some people will promote faster than others. Generally, once you reach a black belt rank, there becomes time restrictions before you can promote to the next Dan ranking. I know an Aikido Sensei who has over 40 years of Aikido experience, and he is a 6th Dan. Most people have a misconception of rank. Again, generally speaking, once you reach 3rd Dan, there is no difference to the next rank and so forth. It is merely "status" and political. You can be recommended for a Dan ranking and be promoted. That does not mean you are any better or know any more than a lesser rank.