Feature Layers fail every second time the page loads, with "Error: Unable to complete operation"

If I create a very simple map based on the Feature Layer On Demand sample, and change the URL to my own feature layer, the map consistently fails every second time:

Error: Unable to complete operation. {code: 400, message: "Unable to complete operation." message: "Unable to draw graphic (null): Unable to complete operation."

If I refresh the page, the layer loads correctly, with no error messages. Refresh it again and the error shows. This applies to multiple layers on the server, not just one, so I don't believe it's related to corrupt geometry or whatever.

I vaguely remember seeing this problem a few years ago, but I can't remember the resolution. The layer is in ArcGIS Server 10.11 and I'm running the simple map via IIS on Windows 7, and accessing it via http://localhost

The only change I've made to the sample is the layer's URL, the map's starting extent, and the infoWindow contents.