It's most likely either your intranet or your minecraft. What version of minecraft do you use? If 1.8 try switching back to 1.7.10 also try closing your minecraft down and logging out then re open it and see if that helps. I had this problem before myself. Also do you use hacked clients?
Can you please give more details. Like does it say something like "ProxyPipe" or unable to resolve hostname? Ways to make sure you're connecting to MineTime properly: 1. Make sure the domain you're connecting with is as followed minetime.com 2. Make sure you have internet connection on the device that you are trying to connect on. 3. Make sure your computer/internet can handle the connection. Depending on how far you live away from Arizona, the connection can either take up a lot of space/mbps or you internet can/might just timeout. 4. Try using different versions of Minecraft. If you're using a modified version use a non modified version. (Hacked clients, client with cape, Optifine etc...) If none of these help then delete Minecraft from your computer. Delete .minecraft, and re-download Minecraft, and try to connect again. If that still doesn't work, well, lucky you.
Well I've had problems like that with the connection, and this worked for me, even though it's seems pretty weird...