12V 120V inverter and battery for off grid oxygen
Your question is "what capacity of batteries do I need to power a 280W 120V load from 12VDC lead-acid Absorbent Glass Mat (AGM) batteries for a given length of time?" 

The rated power draw is 280W. The batteries will discharge to something like 10.5V at the end of discharge, so let's say that the average voltage is 11.2V. Further, let's assume the inverter is 75% efficient. That means the average current will be \$280W \over 11.2V \cdot 0.75\$ = 33A. That means that if the batteries can actually safely (without damage) deliver 75Ah each, the operation time will be about 4.5 hours.

You really need to look at the detailed data for the batteries to see what they recommend for discharge "depth" to see if that assumption is true, but it's unlikely it will operate for more than 4-5 hours. For 8-10 hours of operation you'd need about double that capacity of batteries. AGM batteries generally allow significantly more discharge depth than conventional lead-acid batteries, but it still might be only 80% of the rated amount. 

Note that this assumes that the oxygen concentrator presents a steady 280W load. If the load is intermittent then 280W likely represents the maximum load, and you may get considerably more operating time out of a pair of batteries. There is an inexpensive gadget called a Kill-A-Watt (see Amazon etc.) that can be used to measure the consumption, and it may give you a more reliable number than relying on the nameplate watts. I would definitely make that determination before buying the batteries. 

Here's a portable oxygen concentrator that claims two hours at 2l/min continuous flow (the mode I presume you'd be using at night), using a 98Wh lithium battery, so the average consumption of that product is only about 50W.