I’m running 5.7.1, and ever since 5.7 the library doesn’t update. At one point it said “Last Updated: 4 days ago”. Since then I’ve reinstalled and now it just sits there saying “Pending”.
Also the Up Next List isn’t syncing between iOS and aTV. I started a movie on aTV and it doesn’t show up on the Up Next List on my iPhone. Although when I navigate to the movie on my iPhone it does know that I’ve started it and how much I’ve watched.
A status of Pending means Infuse is waiting for iCloud. One thing you may try is to simply toggle off Settings > iCloud Sync off, restart the Apple TV and then toggle it back on.