Question

Why isolation of staggered and eclipsed forms of ethane at room temperature is not possible?

Answer 1

This is because the energy barrier between the staggered and eclipsed form is very low.

Simply stated, the staggered and eclipsed conformations can be interchanged very easily by providing little amount of energy.

And at room temprature this energy is available so they interchange between eachother easily making it impossible to isolate them.
$.$