As long as you activated the software at some point, you can continue to use the software once your subscription expires.
However, features will become limited if you do not have a current subscription.
If your subscription expires, you will continue to have access to the basic award search, viewing family trees, viewing and saving images, the Judges Handbook and most of the help menu. The "Check for Updates" feature under the help menu will not work without a current subscription.
If you need to renew your subscription, you can do so while renewing your membership or directly from the online store.