Hello from Jeff
I have a 2003 honda Jazz and my problem started with when I slowed down and then accelerated again the car would lurch and jump and hesitate, until it picked up.
Now it has worsened to the point that when I slow down it cuts out and I have to coast to the side of the road and then restart.
My immediate thought was fuel pump or filter, but when travelling along at say 100Kph or 60 mph and I accelerate hard it behaves fine ???

 

maybe you have a clutch problem !! did u see a mechanic for it ?

 

automatic gear box