UPS Problem and Recommendation

Looking for a little direction here:

Our JS12 runs in a BCS which has 4 950 watt power supplies. I configured the power in the BCS so that there is redundancy on a possible power supply failure. I also have two 1500 KVA UPS units backing up the 4 power supplies (two redundantly on each UPS) . So, theoretically, I'd have to have both UPS's fail or completely discharge in a power outage in order for the BCS to lose power. Seems pretty fail safe to me. Except, it isn't. The *slightest* flicker of electricity and the BCS drops like a rock. So, I am trying to figure out what the issue is. Both UPS's seem to be operating normally (I haven't run a test yet because I don't want to lose the BCS during the day). The LED's aren't showing battery failure or any issues. The UPS's are Tripplite OMNIVS1500. I believe one of the two UPS's could be flaky but I'll have to run a self test and that means they will switch over to battery power during the test and if one of them is bad, I may lose the BCS again and I don't want to do that during the day.

The thing that comes to mind is that perhaps the power supply redundancy requires a particular configuration of UPS cabling that I have somehow gotten wrong. I can't seem to find a diagram on how the redundancy is configured on the BCS. Does the power supply in Bay 1 fail over to Bay 2 or does it fail over to Bay3? I am guessing 1 is redundant to 2 and 3 is redundant to 4 but I can't find anything that confirms it. If I have a bad UPS and the power supply and it's redundant twin are BOTH plugged into the same UPS, will that cause the BCS to go down? All of the failure scenarios spelled out in the help text describe losing power to *one* power supply. If a UPS fails and two power supplies lose power, does the BCS go down as well. The BCS is configured with "AC Power Source Redundancy with Blade Throttling Allowed"

Just trying to get to the bottom of the "flicker and die" phenomenon I am experiencing. Any suggestions?