This kind of behavior is usually programmed to happen when the remote system receives a lot of requests from your IP address. Since ISPs do not allocate the same public IP to more than one customer at a time, except for mobile connection, it is most likely coming from something in your home.
If you don't notice the problem on other sites, you should contact the site to double-check with them why it happens.
Otherwise, if you're on a mobile connection, you could contact your provider to get a public IP, but they may refuse or charge more for it. If it's not a mobile connection, then most likely one of your devices is doing a lot of requests to that site and you should look into that. It could be caused by many things including spyware or simply your family using the site abundantly.
1The "Attention Required" page is generated by CloudFlare, which is used by many websites. It seems there might be an issue at your IP address; make sure there isn't something on your network that's doing odd things. – bwDraco – 2016-04-27T19:54:10.493