If I cancel my subscription, do I need to keep the subscription active to access my form?

If we upgrade to the $19/month option, can we cancel when we don't need the form service or do we need to keep it to have access to what we've already created?

If you upgrade your account and for any reason you decide to cancel, then you will have access to your form and submitted info, but do note that the limits for the free account will be applied so you may receive the message that you're over limit depending on the limit you've exceeded. 

If you have exceeded the submissions storage limit when you downgrade to free, then I would suggest you to download your data so you do note lose anything, this guide will help with that: https://www.jotform.com/help/374-How-to-export-all-of-your-data-at-once 

If you have exceeded the submissions, views or active forms limit then you would need to wait until the counter resets or upgrade your account again. 

If you exceed the available upload space, then simply downloading the uploaded files and deleting the submission related to the file will help to get free space.