How can I prevent frosting from pulling off the top layer of a cake?

put it in the microwave for a few sec, make it softer to spread

Let the cake cool completely. You may even want to stick it in the fridge for a bit. Then, do a very thin "crumb layer" of icing. Let that sit for a few minutes in the fridge and then proceed with frosting the cake. :)

Do you mean while you are applying the frosting? If so, then plop frosting in the center of the top layer and gently work it out to the edges. Always use a light touch. If you mean it slips off the cake while cutting slices, make sure your cake is at room temperature and it shouldn't separate.

The cake has to be completely cooled,

Dee of Georgia is right (if that is your question) and also Ficher Luce of California. Both are good tips. If you are meaning how to keep it on while transporting the cake, stick some toothpicks in the top of the cake then drape the clingwrap on top. Some women place mini marshmallows on the tips of the picks so they don't pierce the wrap.

Absolutely be certain that your cake and your frosting is room temperature that should allow for is in spreadability without taking the top of your cake off your cake once you start spreading the frosting with a knife. The other thing that will help is to have a cup of, room temperature water, and every once in awhile... you can dip the knife in the water. This allow the icing to spread smoothly... without any hiccups along the way.