My contribution pages have gone blank
Ok, so here is where I am after some head scratching and some inspiration from @IowaBoy. All of my contribution pages are now working, having recreated the problem ones from scratch instead of copying a working one. All of the contribution pages that had problems were created about a year ago and they were working as we had membership sign-ups from all of them. I now think that they stopped working after my upgrade from CiviCRM 4.7.27 to 4.7.29. I suspect this as that I started receiving notifications about the problem some time after the upgrade. 

In my investigation of the problem, I verified that a new test contribution page made by copying the working one also did not work. I further verified that a new test contribution page made from scratch worked as expected. I have recreated our non-working contribution pages from scratch and so far they seem to be working. I stronly suspect that something in the 4.7.29 release has broken the process of creating a contribution page by copying. Thanks to IowaBoy for stimulating my thinking process.