If I can't find the hole causing a flat tire, do I need to replace the tube?
Sometimes it can be hard to find a small hole. Sometimes it helps to mix water and dish soap together and either pour that over the partially inflated tire, scanning for leaks or submerging the tire in a bucket of soapy water.  The soap will bubble and make holes more apparent.  You also probably want to immerse the valve to see if the leak may be originating from there.

If the problem is coming from the valve, then you will want to go ahead and just replace the tube.