[Vuejs]-Get the value of a prop of the before instance Vue

As you have stated, re-rendering means just that…rendering again. 🙂
So the short answer would be no, you can not save prop value within a component and use it after re-rendering.

You say that every minute you are fetching some data that later on you will be doing some logic on. As suggested use Vuex for that, save that data before re-rendering and the use it as you like.

One of many Vue.JS good point is a very well written documentation. You need Vuex so here it is: https://vuex.vuejs.org/