I renew books as long as nobody has a hold on them. I do require that the student physically bring the book to the library to renew it. Some students may try to hide the fact that they can't find their book, and just keep on renewing. This helps me determine lost books earlier.
When the student is renewing the book, I'll ask about how far they've read or whether they like the book so far. Sometimes they realize it's not a book they care to finish or slog through. Then it's better to choose a new book.
I find that elementary students don't need to renew their books so much, unless they are reading something as huge as Redwall books.