If a character is restrained or unconscious/sleeping, do they lose any bonus from dexterity for armor class and dexterity saves?
AC calculations do not change, however you do automatically fail strength and dex saves (PHB 292).
AC calculations do not change based on your state of consciousness or other conditions. You will grant advantage on attacks, but your armor calculations don't change.
This is likely for ease of use rather than any kind of mechanical simulation.
Generally, AC calculations are something you do once when you level up (generally it only changes if you get an ability increase related to ac or take a feat so that's pretty obvious) or get new gear and do not change (though as a commenter points out you may need to keep a record of your unarmored ac if your DM plans to gank you in your sleep). Unless something specifically grants a bonus/penalty, AC is going to be constant.
With the automatic failure of dex/str saves, you don't have to worry about any bonuses to those saves, you simply fail them.