I don't think 7 games is enough if a player is giving 100% and there are signs of improvement.
In Sahin's case, despite his reputation, he showed very little and I think in games like against Everton it became very clear he wasn't up for the physical side of things. It doesn't take very long to figure out someone's mindset and commitment. I think that's the decision Rodgers took on Sahin and it was the right one.