Backup causing critical error

I tried to take a backup of the site last night and it took ages. The log said error so I cancelled it. The site then threw a critical error, but I got no admin email.

Logged on this morning and site had gone back to normal, thankfully. I went to take a backup and the same thing happened. Again, no admin email. Would appreciate some guidance on how to fix it.

The page I need help with: [log in to see the link]