Question

Explain why a second determination of the melting point should not be performed on the resolidified sample used for the first determination?

Answer 1

I think the original melting process may drive out some of the impurities in the sample and those condense in the upper part of the tube; therefore, taking the m.p. a second time means we are using a "different" sample

In reality you probably could, however it is not good science as it has been considered to be contamined or already used and a new substance or solution should be obtained.

Hope this answer was helpful in clearing your doubts about the concept :)