If you are still using the Instagram BETA app for Windows Phone that has not been updated since March 2014, you might be experiencing an issue where the app is not refreshing your feeds. A number of users of the app have sent in reports on this activity to Windows Central over the past few days, and it's also been reported on other outlets as well.
While there's no official word as to the cause of this problem, it's possible that Instagram's recent update to allow landscape and portrait images to be uploaded and viewed in its official iOS and Android apps might have something to do with it.
In any case, since Instagram has not bothered to update their official Windows Phone app in well over a year, we would highly suggest using a third-party app instead. Our favorite remains Rudy Huyn's 6tag, which just got updated to allow for uploading and viewing of Instagram's new image formats.
Thanks to everyone for the tips!