This is an old post but people may find it on the internet and we don't want them doing silly things either.
DirSync Cookies to do not expire. They are a point in time representation of the replication state. I have grabbed cookies that were a year old and would just return changes that occurred since that cookie was created. I regularly use older cookies to dig through changes that occurred since 1 month ago, 3 months ago, 6 months ago, etc.
DirSync Cookie data would only be corrupted if someone screwed up the writing of the cookie from what they received from the domain controller or someone modified the cookie blob after the fact.
You do no have to worry about getting duplicate information if hitting different domain controllers UNLESS the domain controller just cannot use the cookie and has to resend everything from the beginning again which is stated in the documentation but I personally have never seen in years using DirSync. The cookie gives state for a specific domain controller but that also has information across the entire domain (or NC being synced) for other domain controllers.