Website often down despite being rebuilt and optimised with Hummingbird and Smush

This site – http://abbotshouse.co.uk – often reports as being down. We’ve since optimised the site with better php maximum values (by our host) and optimised via Hummingbird and Smush yet it still reports as being down a couple times this morning already (though when I check, the site is ok)

Can you investigate and advise please? Thanks!