How can you maximise the shell life of milk in milk bags, after having opened them? My grandmother buys milk bags as they cost less, stores each milk bag in a pitcher as such, but can drink only 1/4 of the milk bag daily. So after opening each bag, she must close and fasten the milk bag, and to do so she has tried using a rubber band and a binder clip.

The problem: Rubber bands and clips fail to be secure enough, since the milk always start to spoil on the 4th day. 
So what else can be used to close the bag, to increase the endurance of the milk in the refrigerator?
Nothing at all. It doesn't matter how you close the milk, 3-5 days in the refrigerator is the time it will last in the refrigerator. 

If your grandmother wants to spend less money on milk, she will have to buy it in smaller packages. Even if they cost more per unit, she'll have to calculate the price when taking in account the waste from the bag.