You keep going. Not sure if you want to here my story but I'm one who walked away. I'd started on the thesis. I actually had one paper published and another submitted, so there was the bones of it, but alas. I guess my problem was that I started at uni in a surveying degree, then picked up an engineering degree because they (the uni) suggested I do. After finishing them, I found myself doing a PhD in Engineering looking at - wait for it - statistcal modelling of cast iron waterpipe failures. How could you ever walk away from that I here you ask? Well, I think the pull of surveying got to strong. It's what I've always wanted to do, and now I've been doing it for a number of years and I'm so glad I'm at where I'm at. Still, I'm always thinking about what it might have been like with all the extras letters around my name. Especially with the drought getting so bad and so much emphasis (compared to before) being placed on water being wasted by leaking pipes! I could have been "THE MAN".
On a lighter note I actually had that second paper published last year, about four years after submitting it! Getting published again brought all the questions re: finishing/not finishing back. My case is kinda special in that I got distracted by the subject I was researching. In that I mean, I went to uni to be a surveyor before being distracted by an engineering degree and then engineering research before finally finding myself in surveying.
So start running hard and writing hard. The relief and joy experienced by holding a bound copy of your thesis ready for submission may be what AF requires for a visit.

Good luck and keep writing, Dr P