Can you help me solve the problem what is wrong with my Nissan Micra 2005?

Ny Nissan Micra ( 2005) keeps cutting out and the battery light comes on, although it is not the battery. It has been towed to the garage 3 times and they put in a new alternator but it has not solved the problem. When it cuts out it won't start with jump leads. It goes ok for a while and all of a sudden it cuts out again. Sometimes it makes a noise for a few seconds before cutting out