@Jemcrystal Are you getting any specific error message when the game does disconnect?
These disconnects could be an issue with bad latency. Below are listed a few things you can do that will help your connection.
To best access The Elder Scrolls Online, configure your router to open the following outbound ports:
TCP / UDP Ports 24100 through 24131
TCP / UDP Ports 24300 through 24331
TCP / UDP Ports 24500 through 24507
TCP Port 80
TCP Port 433
Update the firmware of your router (it is always a good step to take, as it prevents that an outdated firmware interferes on your connection).
Try to put your modem/router far from all electrical devices and do not coil up any excess signal or power cables (to eliminate possible interference problems).