Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun

As gravitational force is a conservative force and workdone by conservative force over a closed loop is Zero. Thus workdone by gravitational force is zero in a complete revolution.

Work-energy theorem, WG=ΔK.E As L=mvr=constant

Thus rA=rB⟹vA=vB=v

So K.EA=K.EB

Hence WG=0 in tracing a path from A to B.

Workdone is zero in some parts of orbit.

Also, r2≠r⟹u≠v

So K.EA≠K.EC

Thus WG≠0

going from A to C.

Overall WG is not zero in any part of orbit but equal to zero in tracing the path between the points where planet has equal speed.