I have just developed another site (http://www.askewshairdressingltd.co.uk) - I have an issue that when clicking around the site sometimes the page will display just a blank white page with no content? I tried in multiple browsers incase of a cache issue, cleared my cache, also ran dev/build, and also doing ?flush=1, i am running 3.4.
The blank page of death would mean you have encountered a PHP error but if display_errors is turned off SS might not be able to handle the error and display the error / 404 page.
Check that display_errors is turned on, or if you are on a production host and you don't want errors displayed check your PHP or apache error logs for the actual message. If its random I'm guessing it could be a issues running out of memory.