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.
If this will not give you risk and you are okay with that, so go for it. Because this issue is not clear enough, dont know if this is on yolodice or on your site either. So I am suggesting that you try to restart your connection and check the ping instead to make sure you connection is good to go for fast rolling on yolodice. I used to have bad connection either but it does not stop like the one you mentioned, only having some slower bet