Thank you for getting in touch.
I will need some more information from you regarding this problem you are experiencing.
Are you on a Mac or Windows machine? What operating system are you running on your machine? What are the specifications of your computer? What is the file size of the project you were working on when the freeze occurred? How many Map Selections are present in the document you are working with?
It would be very helpful if you could send a copy of the .ai file so that I can try to replicate your problem on my end. Have you also tried changing the intervals for recovery data saving in your Adobe Illustrator Preferences under File Handling & Clipboard? By extending this or turning off recovery data for complex documents, you may be able to solve the issue. Often save progress bars are executed in the background so quickly that they go unnoticed but with larger projects, when MAPublisher writes to the .ai file, it can take your machine longer to process the save.
If you could send us an email via our Support Centre (help.avenza.com) referencing your post here with the information I have requested and a copy of your file I can begin looking further into this issue.
GIS Applications Specialist
Avenza Systems Inc.