The ups supply power from battery even when the

It is common on budget systems that to maintain operational windows on UPS supply the inverter can be supplied by the mains and the battery so the unit will cope with the low extremes of input volts.

You may of course have a rectifier fault which would also cause a similar situation.

If the batteries charge ok in the normal time, then this is unlikely.

All of these cheaper units are difficult to repair, they are full of surface mount components and unless it is a simple fault, it is likely to cost more than the unit to investigate the fault and repair it.

APC units come with powerchute software, maybe use this to see if it reports any faults, or offers some other information.

Hope this helps, thanks for using FixYa

your ups needs to be serviced