It is compulsory to make up missed Itikaf only if it was a vowed Itikaf. We have evidence in this hadith that vowed Itikaf should be fulfilled as it is a kind where a Muslim obliged himself to do it as an obedience for his Lord. In it the Messenger PBUH commanded Umar RAA to make up a missed Itikaf and Sawm that he vowed to fulfil.
Narrated Abdullah ibn Umar: Umar (may Allah be pleased with him) took a vow in the pre-Islamic days to spend a night or a day in devotion near the Ka’bah (in the sacred mosque). He asked the Prophet (PBUH) about it. He said: Observe i’tikaf (i.e. spend a night or a day near the Ka’bah) and fast.