Lose internet connection when playing FFXIV:ARR

I'm not exactly sure why this is happening, but only when I'm playing FFXIV about 10 minutes in my internet will lose all connection and I am forced to restart my router in order to get a connection again. I have a 100/10 connection, with two computers. My PC is wired from the router, while the other is wireless. I can watch youtube, twitch, download torrents or anything else. But as soon I start up FFXIV everything goes dark and I see an 'Error 90000'. My ISP sees no problem on their end and no idea why this is happening.

Anyone else running into this problem?