The computer had been using a PSU/SMPS that gave out only about 180 Watts of power so I replaced that with a 300 Watt PSU/SMPS.

Things seem to be fine now so I won't be needing to add a new UPS anytime soon (the UPS in use right now outputs a max of 300 Watts which isn't enough since my system uses up at least 240 Watts and my monitor uses 135 Watts) unless I really need the monitor on during the, now much rarer, power cuts.