According to this post, it is automatically removed after 30 days. In this case, it apparently took a week longer.
Jeff Atwood says this is because:
if we did not, every meta would be littered with dozens of forgotten "featured" questions over time.
Here, Shog9 says after one month:
As of today, MSE featured questions work the same way as featured questions on any per-site meta: they are featured until the tag is manually removed, something newer bumps 'em off, or the system automatically strips the tag (roughly 1 month after it is added).
Which one is it? This SEDE query seems to suggest Shog9 is correct (especially the 'roughly' part). The data shows that the script that removes expired featured tags runs once a week on Saturdays at around 0:00 UTC, and removes tags that were placed 30 days ago or longer. This means that if the tag is added on a Thursday or Friday, it will take an additional week for it to eventually get removed (as 30 days before Saturday is a Thursday). With the SEDE site switcher you can easily check other metas.
Apparently, it doesn't run on Stack Apps, perhaps because it's not a true Meta site; What's the next Script/App/Library of the Month? has been featured continuously since January. (And yes, we could use more submissions, but I digress...)