As @Barnez said, that's how you repair Wordfence if any files are missing or if your installation is corrupt. This is one possible cause.
@graemetw in your case I'd guess your site is actually running out of memory. When we get new WF customers installing our product and they see a white screen, it's usually a site with less than 64 megs of memory that is generating an out of memory error in the error log. You will inevitably run into this issue if you have a site that doesn't have enough memory.
Regards,
Mark.