Even if you had the option of "believes he has taken the club as far as he can" or "considering his options" (like players get). I just feel it would be more realistic than a managers happiness never changing.
I think there should be a drop down menu that allows you to change your "Short Term Happiness" in your profile information.
It seems at though it is always set at "No immediate plans for the future." I've been with MVV Maastricht for 4 seasons and consolidated the club in the Dutch Eredivise...