Hi HICKS Jeremie,
Thank you for reaching Microsoft Community and apologies for the inconvenience this has caused you.
We would like to make sure first that we get the exact picture of the issue. You are using the device through Wi-Fi and while browsing the Internet, you are randomly presented with the "connection was interrupted" error, correct? If yes, may I know the exact error message that you are getting? If possible, take a screenshot of the error and share it to us here.
I would like to clarify also on the exact model of the Surface that you have. Is it a Surface Pro 2 or a Surface Studio 2 or Surface Studio 2+? Please see this page for reference: Find out which Surface model you have - Microsoft Support.
I'd love to provide you with the troubleshooting steps right now to fix the problem. I am afraid that we may have to wait for the above answer first so that we can provide the necessary information. Once we collect all the information, we will formulate the feasible resolution to help you with your case or if we need you to refer to the support that suits your problem. We will be sure to let you know in advance so that you save time.
Kind regards,
Marrion