What is the outside interface of the ASA connected to?
If it's your router connected to the ISP on the outside then you can try to connect to the outside address of the web server on port 80 from the router itself. If you are able to connect that would rule out the ASA or your internal LAN being an issue and you would have focus your attention on the Internet connection. Instead, if it fails you would have to turn your attention to ASA, check the xlate and connection status. A packet trace from the ASA, when the problem is happening, to the web server may help identify the cause.
HTH
Sundar
