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I'm trying to track down what I think might be a network connectivity issue with my two Ecobees and I'm finding that they tend to drop packets when I use the "diagnostics" section on the Wifi menu. My two Ecobees have 89% and 75% signal (based on the info on the screen), but even pinging my wifi router (Asus AC68U) almost always drops one or two packets each time I run the test. It usually averages 30-50ms per ping (which is already really high), and there are almost always 1 or 2 really long ping times or timeouts in each test run. The behavior is exactly the same on both Ecobees, and they're located 1 floor apart and not really near each other.
In contrast, if I join my iPhone to the same wireless network and ping my router (using the fantastic "Fing" app), I get <10ms per ping and never drop a packet. This behavior is also consistent when I'm standing right next to each Ecobee, and my Macbook Pro has even faster ping times with no packet drops in the same locations.
I see the same packet loss on the Ecobee when I try to ping ecobee.com from the base unit, but I've been focusing on pinging my router to avoid any issues on my external network connection.
Has anyone else seen this sort of intermittent connectivity from your Ecobee? Would anyone mind trying it out on their device to see if the behavior is any different? I believe that you can find the ping options by going to menu->Settings->Wifi->Diagnostics.