Sleep or food to become non-essential.

A bed and a curry to illustrate the concepts of tiredness and hunger.
For this month's dilemma you get to choose between either sleep or food to become a non-essential part of life.  However, if you go for 'never get tired', you can still have a snooze if you want to, it's just that it wouldn't be physically necessary.  Taking a rest would be purely an optional choice.

And similarly, if you go for 'never get hungry' then of course you could still eat food, it's just that you wouldn't have to.  Eating would be purely for pleasurable purposes rather than for nutritional purposes.