"Overloaded" and beeping with only 40 watts drawn (of the 390w UPS)

[BillP]

I purchased a brand new APC 700VA 390 watt Back-Up's UPS for my small commsrack in my home office that consists of 3 devices:

•  Fibre Network Termination Device (NTD)
• Ubicquti Edge Router 4 (Router)
• Juniper EX2200 PoE (Switch) - no PoE devices plugged in though.

I installed the Powerchute software to my computer and I monitored the load. With the UPS fully charged these three devices combined take 40 watts of power. I've run some tests and each test I pull the mains from it, the UPS goes into "overloaded" mode and has a constant beeping tone coming from it. So I did various troubleshooting and isolation tests, and found that the cause was the Juniper EX2200 PoE switch, the UPS also failed to work with a number of other PoE switches including Cisco and HP, I swap it out with an EX2200 non-PoE switch or Cisco 2960 non-PoE and the power stays on.

So as evident the PoE switch is at fault here - ok, fair enough.

Is there any explanation as to why the UPS can't handel switching over to the PoE switch even when there is no PoE devices running, and the total draw power from the UPS is <40 watts. I would understand if all 24 or 48 ports had active PoE devices on them, but a very bare setup, <40 watts it drops.

What VA UPS would be required to sustain the change over from Mains to UPS?, 1000?, 1500?.