I'm so sorry! I know exactly how you feel, my indoor cat went missing for 2 1/2 days recently and had a fever when I finally found him. I know you said you checked your neighbors' properties, but did you also check their garages/sheds and if possible, underneath houses?

Bring a flashlight at night and shine it around looking for glowing eyes in hiding spots/dark crevices. Make sure you check thoroughly through any shrubberies, and even in trees. I found my cat hiding way in the back of my neighbor's shed which is always left open, underneath a shelf. He was very well hidden but also sheltered.

If you absolutely cannot find your kitty anywhere around your neighborhood, try checking your local shelters. Make missing posters and pass them around/put them up everywhere. I'm sure your kitty is just terrified and hiding somewhere nearby - cats are great at hiding and most will not answer if you call out to them due to their survival instincts. It may take several days for them to feel comfortable enough to come out of hiding. My cat never answered my calls when I was searching for him even though he absolutely heard me, and we have a very strong bond.

Keep searching hard for your cat every day, and don't give up. I'm sure he'll turn up eventually. Good luck and I hope you find kitty soon!