Engine keeps stoping, but will start if it is pushed. Could it be the fuel pump? It is being push started, or if it is parked on a hill and you put it in neutral and let it roll, it will also start that way. After you get it going it will run for about 3-4 days and then not start again.
Sounds to me like it is as simple as replacing your battery !!!! When a battery becomes weak it tends to loose its ability to hold a charge. Deffinately not the fuel pump ( thank goodness cause there not cheap).
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