In reply to running toilet -- I recently also had a problem with a toilet that would frequently replenish the water in the tank due to a slow leak from the tank into the bowl. In my case I discovered that the leak was caused by water being siphoned from the tank into the overflow stand-pipe due to a crack in the small tubing that runs from the fill valve to the stand-pipe. The tubing looped down into and below the water level in the tank enabling the siphoning to occur.