Computer UPSs are usually marketed as "10 minutes on batteries under full load". If your router takes 1Amp, this is 12VA power consumption, so (in the ideal world) 650VA UPS should power it for (650/12)*10 = 540 minutes, or nine hours.
I would rather "hack" that UPS, and power the router directly from the batteries (leaving the UPS internal electronic to charge it). You would probably need some simple voltage regulator between the batteries and the router, with couple of capacitors acting as a filter.