When graph uses external data request, and that request is created with time-based wiki markup, graph works for a while, but later stops loading.
During page parse, graph json is generated by the parser, and it includes an external URL with dates like these: 2016-03-21-05 -- 2016-04-20-05
The hash of that graph is recorded in the HTML output, and the graph spec itself is stored in the page_props table.
Later, something either regenerates the page, creates a new hash, and starts serving that without updating the page_props table, or, the page_props table is updated without changing cache. When I looked at the broken graph URL, I saw that the hash it was using corresponded to the date value 2016-03-21-09 -- 2016-04-20-09, but the page_props contained the graph for 2016-03-21-05 -- 2016-04-20-05. So it seems the page_props was stored with the earlier-generated value, and the varnish/parser cache was generated with the later ones (4 hours later).