Gadgets missing from "Add gadget" window

Problem

"Add gadget" window doesn't display all gadgets available for an instance of JIRA.
There is no "Load all Gadgets" option in the dialog after 60 seconds.

Actual behavior

Window displays no gadgets or very few. A warning message appears when loading contents for the "Add gadget" window.

Failed to load gadgets

Something went wrong while trying to load the gadgets.

Try Again

JIRA logs:

2015-03-10 10:00:15.749629500 2015-03-10 10:00:15,712 DirectoryEntryResolverThread-7 WARN sysadmin 807x25311x1 1o8lylz 209.203.106.30,165.254.226.146 /rest/config/1.0/directoryitems/local.json [renderer.internal.local.LocalGadgetSpecFactory$Parser] Could not retrieve gadget spec https://site.atlassian.net/rest/gadgets/1.0/g/com.atlassian.jira.gadgets:favourite-filters-gadget/gadgets/favourite-filters-gadget.xml from plugin-provided gadget spec store: null

Notes

The operation takes a long time, and consumes excessive CPU resources.
This puts pressure on the whole instance, and is affected by other users that may be attempting to load other JIRA screens.
In some cases it finishes loading after 50 seconds but after 60 it will timeout and display the error message.

Steps to reproduce:

On affected instances, try to "Add Gadget" in a New Dashboard.
First the message will show:

and after 60 seconds:

Workaround

• Perform the operation again when the site is not being heavily used. A link to "Load all gadgets" should appear in less than 60 seconds and will show the gadgets on later attempts to add gadgets to the same dashboard.
• Restarting JIRA may also help temporarily.