Can progress be saved?

If someone is in the middle of filling out a form, can their progress be saved so they can return to it?

Yes, there are two methods to do it:

1) Saving the data in browsers cache, so the user must return to the same browser and device: https://www.jotform.com/help/227-How-to-Enable-Auto-Fill-on-Forms 

2) Working with a Session ID, so the user can continue anywhere, please check this guide: https://www.jotform.com/help/97-How-to-Save-Forms-and-Continue-Later 

Let us know if you need more help, we will be glad to assist you.