Over the years I have had this problem too.. I can relate... most of the time, I found the problem to be a VERY VERY small leak around the bead... I use a little kids swimming pool... the plastic one you know.. that people give away and filled that and submerge the whole wheel/tire... What I always wanted to try was to set up a camera and use it with the tire submerged and a couple hours later, replay the recording on Fast Forward to see where the bubbles were coming from.... but never got to it... so I went to Plan B especially on rims I was pretty sure were leaking around the bead... and I break the bead on both sides, clean up the beads with steel wool or whatever method you choose and coat the metal and rubber with rubber cement and let it set for a good half hour and then inflated the tire and hope... if that was it, problem solved... you could also replace the valve while the beads are broken and then do a stupid move like I have done and dropped the old valve inside the tire... "eye roll here"..... I don't know how many times I have found a "brad" in the tire as well... magnifying glass? and PS... I had a Sears mower that had a low tire ALL THE TIME.. I never did find the reason for that.... AND finally.. one more thought... usually to find a leak you use "soapy water" but with an extreme slow leak, that makes the problem worse.. use clear water so you can see minute bubbles.....
