Step 1: Understanding the Question
The question asks for the duration of continuous absence from the sittings of a House of Parliament, without permission, that can lead to a member's seat being declared vacant.
Step 2: Constitutional Provision
Article 101(4) of the Constitution of India deals with this issue. It states:
"If for a period of sixty days a member of either House of Parliament is without permission of the House absent from all meetings thereof, the House may declare his seat vacant:
Provided that in computing the said period of sixty days no account shall be taken of any period during which the House is prorogued or is adjourned for more than four consecutive days."
Step 3: Final Answer
The specified period of absence is 60 days. Therefore, option (C) is the correct answer.