Scheduled posts set as sticky automatically lose sticky once published

I have a client who likes to rely heavily on sticky posts. We have set up a widget that displays the top two most recent sticky posts at the top of their home page. The client has reported problems when trying to schedule a sticky post. Once the publish date and time comes, the post goes into the widget, but then immediately comes out. I have confirmed that scheduled posts set to sticky lose the sticky designation as soon as they are published. If I set an already published post to sticky, it stays sticky until I unset it and is displayed in the widget as expected. (I mention the custom widget only because normally the most recently published post and the most recently published post marked sticky would be indistinguishable — they would be the same thing, so you might not notice that the post was not actually sticky until the next post came in. It shouldn’t have anything to do with the problem, as it only looks for what is sticky and doesn’t go around trying to set or unset things as sticky.) These are the steps I take:

• Create a new post with a publish date 5 minutes in the future and set to sticky
• Wait 5 minutes
• Refresh posts admin page
• See that post is no longer set to sticky

This is happening both in my development environment using 4.5.3 and on the staging and production servers running 4.6.1.
I wonder if anyone else is experiencing this issue?