Honestly I haven't the first idea why this would be happening intermittently as it is, and in the past anything like this was associated with a firewall (commonly ZA) somehow getting amnesia even though an application was allowed access nothing happened, deletion of the ashwebsv.exe entry forces it to ask again and restored things to normal.
I have had the same happen on my firewall once and whilst browsing suddenly no more access, same firefox symptom, checked firewall ashwebsv.exe allowed access, deleted entry, answered yes and bingo back in business.
Now the XP firewall (if it can be accurately called that) doesn't have outbound protection, however, it may still have an entry for ashwebsv.exe. I think the manual setup to use the web shield proxy may be you best bet.
How to disable transparent web shield proxy and allow only those browsers you want use it:
In avast! go to Web Shield provider, Customize..., Basic tab, blank the redirected HTTP port field (remove the 80). Now no browser can use webshield unless you manually configure it to use Web Shield.
For IE - broadband users: -
Tutorial - Web Shield Proxy Set-up for IE. I don't know if this is correct for IE7, I don't use it.
For Firefox users -
Tutorial - Web Shield Proxy Set-up for FirefoxAs final aside, I believe you should be using a full firewall. Whilst the windows XP firewall is usually good at keeping your ports stealthed (hidden) it provides no outbound protection and you should consider a third party firewall.
Any malware that manages to get past your defences will have free reign to connect to the internet to either download more of the same, pass your personal data (sensitive or otherwise, user names, passwords, keylogger retrieved data, etc.) or open a backdoor to your computer, so outbound protection is essential.