The S/R numbers in the upper right corner that show the amount of data sent/received per second? They bounce all over the place all the time... always see the send drop to 0, don't recall if I ever notice receive dropping to zero that often when out in the world. It does it a lot when in my room though, especially once I go AFK (server automatically polls only once every ~300ms, so you should see it hit 0 some if things are fully idle). So, it may depend on what is going on around you I guess?

Otherwise, something may be blocking some of the keep-alive data from getting through. Since you know the IP of your server, you could check your firewall logs to see if something is getting blocked, then try adding a rule to enable/allow all traffic for that IP as well as the lobby servers (the DNS names are neolobby01.ffxiv.com through to neolobby06.ffxiv.com). For that matter, you could just do the entire subnet. It's all leased by SE, and there are several servers in that range that are used for patching, sign-in, think even the mogstation is hosted in that range as well.