I was just like your wife when I lost my cat...it took a very long time to let go. I am still not over it and it was over 2 years ago...especially since it was my fault that he got out in the first place. Similar situation as you...I lost my poor boy on my vacation property in upstate NY. I did the same thing as you and your wife...going out all times of day and night...dusk and dawn to search for him on foot and by car. I made awesome flyers and posters and went door to door everywhere. I was so confident that I would find him. That first night I went out and reminded myself how dark and desolate it is...nobody's going to see him. And I was right...I never even got a one call about a sighting. As a matter of fact I had owned the place about 8 years at the time and I had never even seen a cat up there!
I took all my vacation time to try to look for him...it was heartbreaking leaving the area to go home knowing that he is out there somewhere. I did a ton of research on lost cats and when they get out they tend to stay in the vicinity.....at first. They may get chased out of the territory by other cats, dogs, predators, people and then they end up far far from home. Often, their mentality changes when they are "lost"...there is something called the lost cat syndrome and if your cat reverts to that it's extremely hard to get them back ...the only way is to trap them. I bought 3 wildlife cameras and high powered flashlights and set up feeding stations all around town. I was sneaking around and quite frankly trespassing routinely. Much like your wife I was consumed with finding my cat and I was confident I would...at first. Finding anything in the country though is like searching for a needle in a haystack. Very quickly I realized how difficult this was going to be...but if anyone could of found him..I would of..the things I've listed are just the tip of the iceberg of what efforts I made to try to track my cat Mooch down.
I know you are exhausted...I was too...but I couldn't stop searching until I was forced to when I had to shut the place down for the winter...I suspect your wife will not stop searching until she feels that all hope is lost.
I'll say one thing...the worst thing you can do (in my opinion) is to have anyone say to her...oh don't worry he's found another home by now..I'm sure someone took him in. Sadly when a cat goes missing, most oftentimes it doesn't work out like that so saying that does not bring any comfort. To me it just meant I should just forget about him since he's warm and comfy in a new home...and when you do the research that is not what happens to lost cats. =(
Not sure if I helped you any but wanted to share my similar experience. It is heartbreaking the never knowing and of the guilt that goes along with the cat getting out.
Just a quick question though...did you and your wife look for the cat in all the neighbor's property? In the beginning your guy would not have been far from his home. But you have to look through the neighbors property and buildings...you can't rely on them to...that's where you need the high powered flashlights. Also, your wife is receiving encouragement because cats are great survivors and have been know to be found many months and even years later.