How do electrons lose their kinetic energy in ideal wire? Electrons keep accelerating due to the electric field (produced by the battery) along the circuit. So electrons gain kinetic energy, hence their drift velocity changes. But this is not the case: electrons flow in average with constant drift speed so they must lose kinetic energy. So how do electrons lose their kinetic energy in ideal wire?
Since there is no resistance in ideal wire, there would be no collisions. So how do electrons lose their kinetic energy?
 A: Well, they don't.
An ideal wire would have no resistance so no charge carrier electron collisions with the wire lattice electrons. This would mean that no energy is lost, similar to assuming no friction on an ideal surface.
It could mean that electrons have the speed of light as drift speed. This idea probably doesn't sound right! That's because the wires are ideal, not real. In reality, they would lose kinetic energy.
As an analogy, if you rolled a ball on an ideal surface without friction, it would keep going in theory. But realistically, this real surface would have friction and the ball would lose kinetic energy.
We make these ideal assumptions to simplify problems, not to represent reality.
A: You are asking about a perfect conductor:


*

*zero electrical resistance, a steady current will flow without losing energy

*requires a constant magnetic flux, inside the perfect conductor, the magnetic flux must be constant with time. Any external field applied will have no effect to the internal field.


A perfect conductor or perfect electric conductor (PEC) is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric). While perfect electrical conductors do not exist in nature, the concept is a useful model when electrical resistance is negligible compared to other effects. One example is ideal magnetohydrodynamics, the study of perfectly conductive fluids.


As you see in the comments, perfect conductors do not exist. 
The answer is that electrons will not lose their kinetic energy in a perfect conductor. Their drift velocity will be the speed of light. 
Since the perfect conductor needs a constant magnetic flux, that will keep the electrons move infinitely at speed c.
https://en.wikipedia.org/wiki/Perfect_conductor 
