A partner of ours just had a web site outage and didn't notice until I reported it to them. This was a particularly insidious one as the site was showing a page (so it was technically "up"), but the page was completely blank.
These sorts of things have happened to us as well. The site is down or in maintenance mode and we don't discover until a staff member or donor notices.
That's why I just signed up for Down Notifier. One thing I liked about them is they let you look for missing content, so it will detect cases such as the domain in maintenance mode, or pointing to a parked domain page. I'm not sure how well it works, so you may wish to explore some other options.