The term of the Prime Minister is not fixed and he holds office during the pleasure of the president. However, this does not mean that the president can dismiss the Prime Minister at any time. So long as the Prime Minister enjoys the majority support in the Lok Sabha, he cannot be dismissed by the President.

However, if he loses the confidence of the Lok Sabha, he must resign or the President can dismiss him Since the Prime Minister stands at the head of the council of ministers, the other ministers cannot function when the Prime Minister resigns or dies. In other words, the resignation or death of an incumbent Prime Minister automatically dissolves the council of ministers and thereby generates a vacuum.

The resignation or death of any other minister, on the other hand, merely creates a vacancy which the Prime Minister may or may not like to fill.

Sources: Laxmikanth