I am experiencing this issue too and after downloading the latest version and uninstalling and reinstalling Eset three times I have run out of ideas. The problem seems to occur after the Mac goes to sleep, I get about 5 minutes after wake-up before HTTP access is shutdown. When the problem occurs all HTTP access is broken for hosts on the local network and all Internet sites. If I kill the Eset processes (especially Eset_proxy) then the browser springs back into life and I can browse in Safari or Chrome unimpeded.
Any help to resolve this issue would be greatly appreciated.