First, I apologize for responding to such an old comment but the thread as been awakened by another user so anything is fair game
I’ve had this issue from time to time, that of not being able to ping or SSH to the pi yet my stats page continues to indicate that it has received data in the previous minute.
Those times I’m not in house, I find that it “heals” over time. Normally though I just restart the Pi with a power cycle.
I believe the problem has something to do with waking up a computer which has gone to sleep while Firefox is on the local Dump1090 web page. I saw this happen when I was running the original Piaware supplied Dump1090 and more recently with Dump1090-Mutability and Lighttpd. FWIW, my Pi is mounted outside and connected to my network with a wireless adapter. Unfortunately (or perhaps, fortunately) the situation does not occur often enough so as to get a handle on what might be the actual cause.