You should play 60 minutes this week to increase gameshape.
Reason being that it isn't 100% confirmed that the previous week's minutes is taken in to account.
And EVEN IF the previous week's minutes are taken in to account, next week you will have to play 90 minutes to average it out.
So just play 60 minutes this week and you will be fine.
If his last sign in date was 10th December, then the 6th economic update occurs on this Monday (there hasn't been 6 economic updates since he was inactive for the week). So this Monday his team will go bot if he doesn't log in by then.