If I can't find the hole causing a flat tire, do I need to replace the tube? My back tire got flat. If I pump it up now, it can hold the air for about 30 minutes to an hour before it's totally flat.

I took out the inner-tube yesterday, pump in a bit air and put it into water, trying to find a hole but couldn't find anything.

Could it be that the tire is too old and I must replace it? 

EDIT: thanks to all your response. Beside soap water, I found out hot water is really helpful and that was what I used to fix my tire. There was a very tiny hole on the tube that I couldn't find when I used room temperature water.
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.