Whenever I look in Chrome\'s console, I see this error message:
Site cannot be installed: the page is not served from a secure origin
2019-Dec update: this answer is outdated. Neither of the two flags mentioned in it are available in Chrome any more. Old answer below.
This error is caused by sites served over HTTP if "Add to shelf" is enabled in chrome://flags.
Solution: go to chrome://flags/#enable-app-banners
(used to be chrome://flags/#enable-add-to-shelf
) and change "Enabled" to "Default", then relaunch Chrome.