I own a 2012 SRX and it has started doing the same thing you have described. The car battery is 8 months old and I changed both key FOBs yesterday and the non-starting issue still persisted. In fact, the key FOB was not detected but it never showed "Low battery" or anything like that on the screen. It only said "service air bag" (WTF?)
I took the battery shroud (cover) off just to look at the connections and put it back on. Coincidentally, after I did that, the car started reacting to the key FOB differently. The blinker lights reacted to the unlock / lock commands from the FOB as they should. Prior to that, only one blinker light would flash...passenger side light on the front and the driver's side light on the rear. Then I noticed the car mileage on the screen showed up, which is a sign that you can now start the vehicle when the brake is pushed.
All of this was yesterday while I was stranded at work. And now this morning at home, I went up to the car and the door wouldn't unlock when I pulled the handle. This is a sign that the FOB is not detected. The only thing it would do is unlock the doors (just like yesterday) but could not start the car. The same "1 click" sound that you had and like yesterday.
I popped the hood to see if looking at the battery again could produce the same magic as yesterday. Sure enough, as soon as I did that, the mileage showed up on the screen and I knew I could now start the car. Sure enough it did start.
Bottom line here is....now I don't trust the car at all to be reliable - to start when needed, without putting on my tin-foil hat and doing a martian dance or something. Very frustrating.
Hi, not sure if you already figured out your problem, but I'll share my experience. I have a 2015 SRX with about 27k miles. Same problem, intermitent only. Car would be fine one minute, drive around, stop somewhere, now it won't start. Would wait anywhere from 30 minutes to 1.5 hrs and car would start again just fine as it never happened. Took several videos to show the symptoms. Took to the cadi shop, they said it was keyfob battery, replaced, that was not it. During another time I was stranded, took to shop and next they said it was the car battery, replaced battery, nope, that was not it. finally they got a 'master mechanic' involved, kept the car a few days. I showed them all the video I had. I was told the problem turned out to be the positive red cable going from the battery to the car. not sure exactly what was wrong with it, but it was replaced and tighten I guess. they even took a video themselves of when the car was running, they wiggled the battery cable by hand and the car died. I've now had the car back for about a week and no problem since. Hope this helps somebody because it was not an easy one to figure out.