Fill the tub with water submerge the inflated tube (inflated more, like twice it's uninflated size), and check carefully each section holding it submerged.

If it's not observable, then place some sticks and a heavy object to submerge the whole tube and watch closely as the water is very still. Also look for small bubbles of air forming on the surface of the tube. Wipe them off while submerged and see if they reappear (those bubbles maybe is the air trapped in dust particles on the surface of the tube while you submerged it, so wiping them will ensure that is coming from inside the tube).. that is porosity of the tube.

If you have porosity, replace the tube, if the valve is leaking replace the core or tube, if valve-tube seam is leaking replace tube. If a tiny hole is found, patch it.

If it's not visible any air whatsoever, and still deflates change it anyway, but i doubt it leaks any significant amount over usable time.. a tire that deflates in a month or two is not so bad.