A more complex, but perhaps better solution, UI-wise: HN could just poke Coral/Google/whoever to cache any site that hits the front page, so there'll be a guaranteed fallback--and then switch the link out for the fallback when you press your hypothetical pause button. (The only problem being that this works for web pages, but won't do much to help web apps.)
>switch the link out for the fallback when you press your hypothetical pause button //
I think this interferes too much. An icon indicating that the site is having problems and a second link to a cache would, IMO, be preferable. Such caches in my country are almost certainly copyright infringing if used to redirect users away from the original source - with this modified solution the user chooses. TBH it's probably still strictly a copyright infringement but the situation looks more ethical.
Of course we know that HN won't implement something like this.