The recourse taken by the professor is to the section 1 of the Contract Act. The saving clause of the provision states that the Act wouldn't affect the legality of any custom, unless the custom or other local methods is inconsistent with the Act. Hence the Contract Act is wider than the subject matter and methods of contracting it provides.
The question that is open for discussion is, what is significance of survival clause and how it can be justified in view of Indian Contract Act? Would the performance of such contracts still be pending unless the confidentiality term is expired.
As suggested by the professor, there is no provision in Indian Contract Act about the survival clause or similar clauses and so did he find his recourse in saving clause of section 1 of the Act. In my opinion, there is nothing in contract Act which is against the survival clause of a contract. I would also take recourse to the section 1 of the Act, however, "not inconsistent" part of the same. I don't see anything in Indian Contract Act which put such survival clause into question. I am not sure about the custom of Survival clause itself, however, if it is there since long, it is beyond doubt that the custom part of saving clause also rescue the matter.
Having said all this, I am still curious to know about the significance of Survival Clause and its special stature in contracts. In my opinion, the provisions of indemnity and other provisions related to breach of contracts (S. 73) are sufficient to provide the protection to party. Other provisions of continuing guarantee in the Act also give sufficient protection.
Taking the crux to question: Indian Contract Act says nothing about the survival clause in particular, however, reading definition of Contract together saving clause of Act, it very much ca be evolved. On the second part of the question, even if survival clause is not there in the contract and confidentiality is extended beyond the performance of one of the promises, the contract subsist to the extent of confidentiality protection. In other instance of presence of survival clause, the contract in whole would subsist, not just the "survival clause" despite the performance of chief subject matter of the Contract.
I am open to suggestion on this by readers as I am curious to have explanation of some unanswered questions. To the rest, I agree with Professor.