Probably you have a dynamic IP. Even in broadband it will probably hop. You need to get a site with a fixed IP and then all your visitors to that site get redirected to your pc. You'll need a script that updates the redirect IP of that site.
To save on all this problems I would recomend you get a apache/php/mysql host with a dedicated IP. Those are always online and will cost you the electricity to run you PC (really cheap). If disk space is an issue then you should have both. A dedicated host to run you page from and you PC to store heavy data. Again your PC will need to tell your host what its IP is about every hour or so to be sure.
Saludos
Gerardo