The HD6xxx series has reached peak optimisation and been moved to legacy status, there will not be any further driver updates for your product. More information available here.
The latest Crimson driver for your system is 16.2.1 and is available here.
The last Catalyst driver for your system is 15.11.1 Beta and is available here.
I would recommend using DDU to sweep your system of AMD drivers, and then trying either or both of the drivers above to see if they resolve your issue.
Same problem here and I have too an AMD Radeon HD6000 series (6450).
I used every driver versions available for this card (Catalyst WHQL, Crimson Beta, Windows Update one), but I still have the problem.
A question: do you have a single monitor or a multi-monitor setup?