As soon as event registration was started but not finished, there should be a message in the bottom right corner about this with a link to continue. If user tries to start event registration again by going to event page and clicking Register, he should be directed back to his unfinished registration.
If it works somehow else, it might be a bug - can you provide more details either here or write to support@wildapricot.com.
Evgeny
Product Design Team