Every UPS has a limit and can only supply power for limited devices only .
when a UPS fails you will have to check for the folloeing things
as earlier see if you have connected many devices to the same UPS ,that is more that it's capability.
A standard home use UPS will supply for a monitor , a cpu, a speaker ,a mouse and a keyboard.
Devices such as broadband modems can cause problems when connected to the same ups , since the UPS cannot supply enough power so try disconnecting devices like your modem etc.
Check the fuse of the UPS .
check the battery of the UPS for leakage or short circuitary .
If every thing seems right then try charging your UPS for a whole day and then try.Then contact your provider.