[troyb]

Is it the same site or does it only happen once for each site?

If it's the same site, in Keychain Access, double click on the entry for this site and select the Access Control tab. Does OmniWeb appear in the list?

If it's different sites, OmniWeb will ask once for each site you access but once this is done, assuming you're on 5.7 and 10.5.2, you won't get asked again, even after updating OmniWeb.