it would be helpful if you could name some example web sites and provide a screenshot of the error you receive.
This is a site where this error occur - from the log:
08:47:03.684: Accepted connection on 10.35.40.20:8080 from 255.255.255.255:0
08:47:03.685: Received 363 bytes
GET http://www.onsnorway.no/css/Navigation.css HTTP/1.1
User-Agent: Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0)
Accept-Encoding: gzip, deflate
08:47:03.690: Send: errno: 104 - 'Connection reset by peer' (104); offset = 0
08:47:03.692: Shutdown with error 107
08:47:03.694: Releasing and closing FD (0)
the error seems to indicate that the connection is closed by the remote host, so this could be some kind of network related issue. A packet capture of the connection would be helpful. Probably it is a good idea to raise a service request with support to have the issue analysed? I recommend to provide them with a feedback and a packet capture showing the issue.
As an alternative you can upload the packet capture to ftp.webwasher.com/incoming and let me know the file name and I can have a quick look if there is something noticable. If you need help taking the packet capture please let me know.