Apc backup time calculation
A critical piece of information is missing here: battery voltage. Though it is probably 12 V lead-acid, you should state it clearly just to be sure.

Assuming this is correct, then you have approximately 173 Wh of capacity. Your router presents a 6 W load and your monitor a 24.7 W load, so a total of 30.7 W. Dividing one by the other, you would get about 5.6 hours of runtime, so your 10 hour figure is already off by a large amount.

Of course this is merely an upper bound on the runtime, under the assumption of 100% efficiency in energy conversion, new and fully charged batteries with the stated capacity (certainly not true for, say, many Chinese manufacturers of 18650 cells which claim absurd capacities like 10 Ah). There’s also an implicit assumption that the power converters involved (in the UPS and the wall-warts) do not consume energy for their operation.

Even assuming the stated capacity is right, note that you’ll need to convert the DC voltage of the batteries to AC, which is later converted to DC again at the wall-warts for the router and monitor. For instance, the 80 Plus standard for PC power supplies requires a minimum of 80% efficiency (and when they meet higher standards, they get awarded progressively higher certification levels like 80 Plus Bronze, Silver, Gold, Platinum and Titanium).

Lacking any other information (and, should you have it, please provide it here so we can make more accurate calculations), we could use 80% as a ballpark efficiency figure for both the UPS and the wall-warts. As such, your UPS would only deliver 80% of its capacity to the wall-warts, and the wall-warts in turn would only be able to use 80% of that energy, so you’re losing 80% * 80% = 64% to power conversion inefficiencies. Therefore, your 5.6 hour runtime would already be reduced to 3.6 hours. The actual figure would depend on the actual efficiencies of the UPS and wall-warts.

Also note that SMPSes generally run better when the load is not far off from its designed maximum load. In your case, a load of merely 30 W is being placed upon a converter capable of 1100 VA/600 W, so at best 5% of the maximum. You’ll hardly get peak efficiency at such a low load.

Even so, you’re reporting an actual runtime that’s nearly half of what was expected. So it seems likely that some capacity degradation on the battery has already taken place. If the batteries are a few years old already and you need the extra runtime, it may suit you to replace them with new ones, but if my assumptions are correct, I wouldn’t expect you to get much over 3 hours of runtime under your setup.

If you’re really interested, and depending on the available equipment and time to invest, there are many measurements you can make to improve these back-of-napkin calculations. With a Kill-A-Watt meter or similar, plus an ammeter, you can determine the actual efficiency of your wall-warts. You could take out the batteries from the UPS after charging and do a capacity test, say by using an appropriate 50 W 12 V load (approximately simulating the actual load due to inefficiencies), and time how long the battery lasts until the battery voltage drops to an end-of-discharge value (10.5 V seems like a reasonable value). Given the 173 Wh expected capacity, a 50 W load should lasts for about 3.5 hours. At least for lithium-ion batteries, if you’re getting less than 80% of the expected runtime, it’s advised that you replace the batteries.