Hi Christopher,
It looks like you are indeed loosing power to the switch even though it is connected to a UPS.
Since you didn't provide much information about the UPS, this is conjecture on my part:
I would surmise that the UPS during normal operation directly connects the inputs to the outputs. When a power failure occurs, a mechanical switch (relay or contactor depending on who you talk to)changes state to connect the output to the inverter which is driven by the batteries. I have seen some UPSs get slower doing that transfer as batteries age. When new, there is no issue but when some years old, the transfer time is slow enough the switch's power supplies can't hold the load up long enough.
Note that the power supply hold time (not the UPS's) depends on what is going on with the switch at the time of power outage. It there a lot of traffic? Are there lots of VoIP phones, especially if people are talking at the time? POE cameras, especially Pan Tilt Zoom (PTZ)? All of these add to the power drain on the switch's power supplies and the UPS.
You can get a definitive answer to this if you can get a small UPS to connect to ONE of the switch's power supplies. (If those are 1400W power supplies, you will need a 2200VA or so UPS.)
When the next power event occurs, if the switch doesn't go down, look at the logs and see if the power supply without the added UPS goes down. If so you have your answer.
If that power supply does not go down, then you can scratch you head some more!
I suspect that the other items connected to the UPS have longer hold over times so they can ride through short (50ms) transfer times without crashing.
James