Just to let you know whenever you pause/hold you subscription and not paying the subscription amount with in that period software only goes on deactivate mode. There is no need to download the software again on you computer after paying your subscription.
Until you uninstall the software from your computer by your own software will remains there in your computer only (in case of deactivate mode as well).
You just need to activate the software using the internet connection after paying the subscription fees to Adobe.