If you've taken a close look at the tire and haven't seen anything out of the ordinary like a cut, tear, nail or screw, your next order of business would be to check the valve stem and core.
Sometimes the valve stem can dry rot and start to leak or the valve stem core can also start to leak from corrosion, gunk or from being cross threaded.
Oftentimes you can miss small screws or nails just as we recently did (see pics). A couple of quick glances had us overlooking the small nail in between the threads. But a closer examination told the entire story-we had been nailed.
When looking over a tire it's best to have someone slowly roll the bike forward while another person looks at the tire, unless you have a rearstand that will enable one person to complete the task. Rotate the tire slowly, looking over the entire span of the carcass, including in between the threads. Many times a closer look will unearth the little bugger that's the root of your problems. From there you can repair the tire or replace the entire hide if needed.