I am planning on making a few small batches of beer (1 gallon) and i don’t want to pitch a whole vial in each batch. I was thinking about making a starter and just adding some to each batch. However, I don’t think I will be able to make all the beer in the same day or same week. Will the yeast starter last for a week or two in the fridge?
The yeast will be fine. Ideally if you let a starter sit for a couple of weeks you’d want to wake it up with some new wort but given the small size of your batches I’m sure it would be fine. The total batches really aren’t much bigger than a starter anyway! 
Probably want to make a pretty big starter though to start off with. What I’d probably do is make the starter, cold crash it in the fridge, and pitch some of it into the first 1 gallon batch you’re making. Then you could toss another couple quarts of starter wort on top of it and let that ferment out to build up more yeast and keep them beasties awake.
It might be easier to pitch about 1/4 of each yeast cake into the next batch.
+1. I would just make a starter with all the vial and either use paart of the slurry for you next batches or collect all the slurry and simply make starters from that. Much easier to control.