This was mentioned in this thread on the twenty-sixth page (https://community.spotify.com/t5/Help-Desktop-Linux-Windows-Web/web-player-not-scrobbling-to-last-fm...) so in the interest of creating a new thread with relevant information towards a targeted issue, I decided to make a new thread.
Recently, Last.fm did a makeover over their entire site UI, and it appears that the Web Player is broken with Last.fm integration. My accounts were linked initially, but I first noticed that my plays weren't scrobbling from the Web Player on Firefox, so I tried disconnecting the accounts and I was going to reconnect them. However, whenever I tried reconnecting the accounts, it would bring me to the Last.fm page to connect the accounts, and I would be immediately redirected back to Spotify after confirming—and there would be no change to the Last.fm status for my account, and it would prompt me to just connect again.
For testing purposes, I disabled my privacy add-on (Ghostery), but it still didn't work. I then tried the exact same operation on stock installations of Google Chrome, Chromium, and the Epiphany web browser, but I ran into the exact same issue on all of the browsers, which is why I am almost certain the issue is with the Last.fm API. All versions of my browsers are the latest as of 2015 Aug 19.
Hopefully this is fixed soon as I only want to listen to music on Spotify if it's being scrobbled. :) Hope to see support added back very soon!