Random 502 error for static website (BB-10777)

We are getting random 502 errors when trying to load a static website. Example url:
http://modernsignal.bitbucket.org/nahb/ibs2015/search-education.html

There is a relatively large number of linked assets, and reloading the page produces a 502 error for a random sampling of them. The last commit was two days ago and it was working after that.