I've attached a copy of their support response:
Dear Andrew,
Thank you for contacting 123-reg on the 28th June 2013.
In the screenshot you provided, this was the following error:
Fatal error: Out of memory (allocated 71041024) (tried to allocate 1966080 bytes) in /websites/123reg/LinuxPackage21/th/at/sy/thatsyourbestbet.com/public_html/wp-content/plugins/w3-total-cache/inc/options/general.php on line 777.
If you look at the folder structure, it states the W3 Total Cache folder/plugin where the error occurred. When the plugin tried to allocate some memory for itself for it to function, there was not enough available hence the 'Out of Memory' error.
As I have said stated in my previous ticket, you can try and disable one of your other plugins if you wish to keep the W3 Total Cache plugin or go with our VPS option as you can increase the amount of memory for PHP to your liking.
If we can be of any further help with regard to this or any other matter, please do not hesitate to contact us.
Kind Regards
Darrell
123-reg