In any work in which you use symbols, you have to establish the scope of each symbol when you use it. There is nothing to say that you can't use the same symbol to mean different things in different places as long as you clearly scope it each time it is used.
On the other hand, you should not assume that if you decide to scope a particular symbol to the whole book that the reader will necessarily recognize that the symbol you use on page 134 is the same one you last mentioned on page 17. Unless you use a symbol consistently and frequently throughout a book, the reader is likely to treat is as local even if you intend it to be global.
So either way, make sure you define your symbols each time you use them, whether you scope them globally or locally.
However, if you have used a symbol to mean one thing on pages 17, 23, 47, 52, 73, and 87, you probably shouldn't use it to mean something different on page 103 because by that point your readers will probably see it as a global symbol even if you have been scoping it locally each time.
Or, to put it another way, consider if your past use of this symbol or of symbols in general suggests to the reader that this or other symbols have a consistent meaning or if it suggests that they have individual local meanings, and use them accordingly.