It is a very sticky subject with no clear cut answer..
I have been working for professional arts organizations for the past couple of years and there have been several occasions where a show has been cancelled due to lack of ticket sales. Of course, this is due to the fact that with the lack of funding, many of these organizations can't afford to lose money on a show. It is also not usually the presenting theatre who cancels, but the actual performing group. They check the daily sales records and if it looks like the show will be a big financial failure they will cancel rather than risk a huge loss. Last year we had a show booked into a 2,500 seat theatre and a week prior to the show only 300 tickets had been sold. The performer decided to back out of their commitment rather than go on and lose money.
In commercial theatre it is all about money, so of course if it means cutting losses then the powers that be will pull the plug. In amateur or educational productions I don't think a show should be cancelled for lack of audience. Most of the time these organizations have paid for the rights up front (or mostly up front) for a certain number of performances and I am not sure how easy it would be to get any of it refunded if they decided to cancel for lack of ticket sales. I think it is also unfair to performers who have put in time excess of their day jobs, who are performing for nothing more than a love of theatre, to have a production they have put in many nights in row to prepare for cancelled.
I volunteered at a community theatre production of Lippa's
John and Jen once and the audience barely outnumbered THAT cast on stage -- but the show went on!
"You pile up enough tomorrows, and you'll find you are left with nothing but a lot of empty yesterdays. I don't know about you, but I'd like to make today worth remembering." --Harold Hill from The Music Man