***** Solved *****
I found a forum post, which I will provide a link for below, that advised finding my AppData folder and deleting the MPmissionCache folder. I did this and was able to successfully log in to the server. I shutdown arma 3 and was able to log in, again, without issue.
Here is the link to the forum post I found.
http://www.506thir.net/forums/index.php?topic=2870.0