I've read that there are issues with this phone/OS *originating* ping - that is NOT the case here. The 'ping' command is never used on the phone. The phone is receiving pings.
Pings are not entirely blocked since it responds correctly for the first few seconds (though not quickly - usually well over 40ms).
This feels - wild guess, could be way off base - more like the GS4 has determined that these pings are some kind of attack and therefore decided to stop responding. Is there anything like that in there? I don't know who would know the internals.
We have not seen the issue with GS3 4.3. We don't currently have any other devices running 4.3, though there is one Galaxy Nexus which could be upgraded.
* Why? Two reasons.
1. The Realtek function which we can call on our computer to determine whether there are any wifi clients connected quite frequently returns false data, and Realtek won't help us. Thus ping is now our method of detecting when the user has walked away.
2. Some older phones (not GS4) are quite sluggish in the ensuing file transfers from our mobile app unless 'prodded' in this manner. We haven't figured out why. It's like they need to be kept awake at a sub-second level.