Make a record of the error. Useful for anyone investigating to have. Not sure what you mean by 'logs out' though if the kernel isn't booting. Is it stopping with an error immediately after grub, is it getting as far as trying to start X?
Akmod and the proprietary Radeon driver are from rpmfusion, it may be worth asking on their mailing list http://lists.rpmfusion.org/mailman/listinfo/rpmfusion-users It's been a while since I've used an akmod, but occassionally they run into problems building and it's worth trying the kmod that matches the kernel and driver version instead.
I tried with kmod too, same problem. The system loads, then it abruptly closes and I see an error like "Sorry, the system crashed" with a log out button. Clicking it does nothing