It's not currently possible to save a partly filled-in questionnaire and return to it later.
This isn't usually a problem as most questionnaires take 5 to 15 minutes to complete, and there's no time limit on submitting a response (as long as the browser window is not closed).
We've had hundreds of thousands of assessments run on Spidergap, and only a tiny minority of customers have had issues here.
That said, we know that - even if it doesn't happen very often - losing a response can be very painful.
Fixing this is one of our top priorities. We are working to add auto-save functionality so that progress is automatically saved as the participant fills in their answers. We'll shout loudly when this feature is released!
In the meantime, if you or a participant is concerned about losing a response (perhaps having spent a lot of time on certain answers), we'd recommend that they save work on their text answers in a text-editor (e.g. Word) and copy them across when ready.