Mix up a cup of soapy water, like you'd use for blowing bubbles.

Pull the tube out of the tire but keep the valve in the rim and one bead of the tire on the rim. That keeps everything lined up so it's easier to find what's making the hole.

Pump the tube up fat and run it through the soapy water. Somewhere, you will find a very small hole.

Line the hole back up with the tire and feel for the problem. (Looking might help, but might not. I find it's usually easiest to find the culprit by feel.)

Then patch the tube, don't replace it.

As for what could be causing the flats, some of the hardest things to find in a tire are small wires that are nearly parallel to the casing threads. They're almost invisible, and they may not stick out enough to see. They only push out of the tire under load to cause the flat, then go back to hiding.