It is unusual that a website would cause your Wireless network to disconnect unless it is running some form of malware / script / exploit which is directly referencing your network setup - I've never heard of any such instances, but it could happen.
A couple of things to try are :
See if you get the same problem with a wired connection
Temporarily turn off the Wireless adapter on your laptop & use a cable directly wired to your router. Visit the website and see if you get the same problem. If so, there seems to be something seriously wrong with what the website is doing to cause your network configurtion to be affected like that - search online to see if anyone else has mentioned similar problems and / or update your browser / Malware protection. If you don't get the same issue when wired, it would imply the website is not the cause of the problem.
See if you get the same problem elsewhere
If you can, use another Wireless connection elsewhere to see if you get the same problem accessing that website. This will help determine if it is a problem with your laptop / the website itself or if the problem is localised to your own Wireless connection. You could also try using another laptop (if one is available) to access the website at the same time as you are having problems to see if that laptop encounters the same issue.
See if you get the problem at a diffrent time of day
Assuming the above didn't cause any problems, try using Wireless & visiting the website at a different time of day. It could be that a neighbour is using their Wireless at the same time and there is conflict between your Wireless networks causing one or the other to drop & need to reconnect. There are only a finite number of radio channels that Wireless can operate on, so if a neighbour turns on their Wireless and conflicts with the channel you are using, this might cause a problem. If you are both creatures of habit and do it at the same time, this may account for the problem.
Hopefully, a combination of the above might help narrow down the cause of (if not solve) the problem. Let us know how you get on.