I would not normally re-use staves.
I use the appropriate amount of oak for the volume of wine I am dealing with. In the end, the oak has given its all and is, therefore, tossed out.
That is not to say that you should not. They do, after all, use a single barrel for multiple batches of wine.
If you do opt to reuse oak, the wood should go directly from one batch of wine to another with, perhaps, a quick rinse in k-meta in between.
I would advise against storing used oak for later use.