I was having the same issue (running PVZ on Windows 7 on iMac dual boot). The game had previously worked fine with no issues, but recently I was getting the message 'Must be signed into Origin to continue' even though I was signed into Origin and had launched the game from inside Origin - very frustrating. I had tried to unistall the game adn reinstalled but that did not solve the issue. After reading the posts in this blog, I started looking at my AV firewall settings. Not an ideal solution, but if I disable my AV firewall, the game connects to Origin and works fine. Problem solved with the game but my firewall is now off.
