The draft lasts until the date you chose for your draft. While creating your invitation, there is a "Date" field and you can input any date in the future to make sure that it is still available. Once that date has passed, your draft will be removed from your "Upcoming Events" list.
If you are unable to find your draft, make sure you are signing in with the email you created the account with, as well as signing in via Evite instead of Facebook if you do not utilize the Facebook sign-in.
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