That would be another video card, without a doubt.
Wouldn't happen to know how long ago it was by any chance? Just wondering if it could be within any extended consumer law coverage following the previous replacement. I can look it up if needed, if you wanted to PM across a serial number.
Otherwise it's a tricky one to work around. I've heard about some affected users removing the GPU kexts from their OS install to prevent the video drivers from loading, using the video card as a frame buffer only, but don't expect any visual effects or anything requiring video acceleration, which is unfortunately almost everything on a Mac these days outside of light web browsing, email and document editing, generally speaking.
There were more reliable cards available for that model iMac with performance as a trade off, such as the AMD Radeon HD 6770M 512MB. Some older Radeon 5000 (2010) series cards may also work but I haven't tried it myself. Some users have managed to get later MXM cards from other manufacturers like Dell working in the iMac as well, albeit without brightness control or boot screens.