01 Cabrio starting/idle issues
 

I am not a VW guy, but my wife wanted a cabrio. Recently, the idle has been fluctuating and the car will not stay running when started unless it is lightly throttled and "warmed up". We have replaced plugs, rotor, cap, etc. The battery is fairly new. Ironically, the outside temperature has not been a factor as the issue has been present in cold and warm environments and has been ok in both also. Help please!!