The correct option is C hasn't been
The present perfect continuous tense (also known as the present perfect progressive tense) shows that something started in the past and is continuing at the present time. Here, the illness of Sid started in the past and continued till present. The present perfect continuous is formed using the construction has/have been + the present participle (root + -ing). Hence, Option C is correct. The rest of the options do not express the relevant tense, hence they're incorrect.