Exception in a Static Constructor

Some days ago, a coworker of mine had a very nasty bug which no one had a immediate explanation for: The problem was that in his application, he was trying to call a service: usually this worked just fine, but when the service was shut down while he started his tool, his application stopped working even tough the service was started right afterwards again.

After some research and debugging, he found the problem and since nobody in my team actually knew that, I think it's worth a post.