Motors "burn out" from two things: Overload, or degradation of winding insulation. If you have confidently eliminated the possibility of overload (and I have no way of knowing your competence to do so), then all that is left is degradation of the insulation from some other means.
Moisture is probably the most common. Most motor insulation is slightly "hygroscopic" meaning it will absorb moisture. Even if used in a dry location, condensation can still be an enemy. If, when the motor is off line, it is exposed to low temperatures and then energized and loaded quickly, that moisture gets behind the insulation and vaporized when heated, causing a "bubble" that eventually breaks down the insulation.
But all of this is conjecture. You have not provided anywhere near enough information to allow us to be of help. What kind of OL relay? What does "we have checked all the parameters regarding single phasing" mean? "Motor rotor winding burnt... " Was this a Wound Rotor Induction Motor then? You didn't mention that before. If so, this is a whole different issue, meaning you can now have brush problems, slip ring problems etc. An OL relay may or may not fully protect the rotor windings on a WRIM.
