In a parliamentary system you don't directly vote for the Prime Minister but indirectly. The Prime Minister is the leader of the party that runs the government and the people vote for the party not the candidate. With the presidential system people vote for a candidates from different parties. If a Prime Minster is replaced or steps down its not as bad because the people didn't vote for that person just the party.

I assume you're restricting your question about presidential systems to America, because lots of other countries have regular resignations of their presidents (for example, South Africa's President Zuma or the Philippines' Duterte)?