The power consumption of 955BE ( OCed around 4 Ghz ) is around ~400W under full cpu load with prime 95 like app without gpu load - now games though don't use cpu like prime 95 modern games can take advantage of multi core cpus very well - so games utilizes cpu resources pretty well ( for eg, games like BFBC2 ) - now when you play games the gpu is also under load - so while playing games your overall power consumption would be around 400W as you have HD6670.
Now the PSU you have is rated at 80% efficiency - so to deliver 400W your PSu draws 480W from wall socket ( in here from UPS ).
your PSu is draws 480W under load - include another 40-50W for monitor and speaker if they are connected with the UPS - the overall power draw around 530W whiuch the UOS has to deliver.
when connected to the wall socket your UPS can flawlessly draw 530-550W from the wall socket to deliver power to the entire system but when there is load shedding your UPS has to deliver 530W but it's only capable of delivering 360w from battery backup - this is the reason why the UPS shut offs the system and beep sound - I think you now know the reason clearly.
The summary : You need a better UPS