Summary
Trust requires mutual respect. Moreover, trust is essential to any long-lasting relationship, personal or professional. Personal relationships, such as marriage or friendship, additionally require natural affinity. If a personal relationship is to last, it must be supported by mutual respect and affinity.
Notable Valid Inferences
A personal relationship supported only by trust and mutual respect will not be long lasting.
A personal relationship supported only by natural affinity will not be long lasting.
A personal relationship supported only by natural affinity will not be long lasting.
A
A friendship supported solely by trust and mutual respect will not be long-lasting.
Must be true. As shown below, a long-lasting personal relationship requires natural affinity in addition to trust and mutual respect. 
B
In the context of any professional relationship, mutual respect presupposes trust.
Could be false. This answer choice confuses sufficiency for necessity. We know that mutual respect is a necessary condition for trust. It is possible for a necessary condition to occur without the sufficient condition.
C
If a personal relationship is supported by mutual respect and affinity, it will last a long time.
Could be false. This answer choice confuses sufficiency for necessity. We know that mutual respect and affinity are necessary conditions for a personal relationship to be long-lasting. It is possible for a necessary condition to occur without the sufficient condition.
D
Personal relationships, such as marriage or friendship, are longer-lasting than professional relationships.
Could be false. The stimulus tells us several necessary conditions for these relationships to be long-lasting, but the stimulus does not give us any information to infer which relationships are longer-lasting than others.
E
Basing a marriage on a natural affinity will ensure that it will endure.
Must be false. The stimulus tells us that personal relationships, such as marriage, require mutual respect in addition to natural affinity.