Is your connection suddenly reconnecting? Sometimes this can be happened as well when you have your connection bad, of course it will auto connect but the rolls wont go anymore because of the restart of your isp. I do not think this is really tiny issue, because you will never know when you are going to hit right? If that moment you are going to hit and it stops, you must saying bad about yolodice. If you do not want this to happen, please fix it with their team, they will give you a solutions here
Maybe, I cannot know,,, everything else is working fine but then I guess Yolo is the only site where it is constantly on a connection, also I know for Yolo if you disconnect there will be an error message saying "Reconnecting" which is good, so I doubt it is about my internet.
It is a tiny issue for me, if I hit, I hit. If we use your argument, we can say what if you are going to bust and the dice stops in time?

I would never say a bad thing about yolodice or any site if it stops, why should I? Just click start again.
I am guessing it is your internet connection same thing happens to me sometimes and i check my ping on cmd i do get disconnections on my internet. Try restarting your router.