Sounds like something happened and you got a stuck fermentation. Maybe it got too cold, maybe the yeast were just lazy. Moving it got them all stirred up again and it continued fermentation.
Or, you're relying on your airlocks to tell you when fermentation is complete and you're seeing CO2 coming out of suspension in your secondary. Are you using a hydrometer to check whether the "fermentation started all over again"? A hydrometer is the only way to tell whether fermentation is actually happening. As Revvy says: An airlock is not an indicator of fermentation.