Available updates not displaying on local copy but show up on live site; instead displays "You're all up to date!" with 5 pending updates When I attempt to display available updates on my local copy, Craft is unable to display them and instead shows “You’re all up-to-date!”. 

Available updates do display on my live copy, as well as on the “updates available” badge on the local copy CP. 

I’ve cleared the cache to no avail and I’ve checked the logs and can’t see any errors. I'm running an nginx server and am starting to wonder if this problem arose when switching from apache -> nginx.

I am currently running version 2.6.2996 and am trying to update to 2.6.3001 as well as update a few plugins. 

Has anyone run into this issue while trying to display updates on their local copy CP?

The responses coming back when I hit the updates page were all 200s and allowAutoUpdates was set to true using the default setting.
Adding my comment as an answer because it fixed my issue:

I traced the issue to a deprecation warning involving $HTTP_RAW_POST_DATA being populated. 

I added the line always_populate_raw_post_data = -1 to my fpm_app.conf which solved the issue.