The valve core (assuming Schrader) is easily replaced. Think they're universal, so any local tire store should have one. Or just replace the tube, and while the tire is off, run a dryer sheet around the inside of the tire to see if there is a thorn or anything in the tire. Dryer sheets are great for this-they will snag on almost anything! Could be that if there is something in the tire/tube, when whatever it is, is positioned so it's on the floor, the pressure from being on the floor is acting like a "plug", allowing only a slow leak. When not on the floor, could allow more air to escape, as there is not pressure on it, so you lose the "plug" effect.