But they can also be taken out much more easily when they lose popular support - see Thatcher, Maggie, Defenestration thereof.
Less dramatic, the removal of Canadian Minister Chrétien by a determined inner party putsch led by Paul Martin, who of course went on to a distinguished career as Prime Minister.
There’s also the worst case example of what Mulroney did to the Progressive Conservative party. In a parliamentary system, the Members of Parliament can’t distance themselves from the PM the way Congresscritters can in the American system. If a PM is deeply unpopular with the voters, the entire party suffers, and individual MPs lose their seats, because the only way to vote against the PM is to vote out your local MP. Mulroney was so unpopular that even though he had resigned as party leader, his successor, Kim Campbell, led the PCs from majority government to 2 seats - the greatest fall in parliamentary history, certainly in Canada and likely in the Commonwealth. This dynamic means that a deeply unpopular PM is likely to get pushed out by the party, and that possibility also means that the party has a greater internal check on the Prime Minister than do the parties in the congressional system.
The best example of the contrast is President Tyler, a Democrat who was chosen by the Whigs as Vice-President candidate to round out the Harrison ticket. When he became President, it turned out that Tyler didn’t really support the Whig agenda, vetoing much of their legislation, but he was also hated by Democrats for leaving them. Sop he was a President without a party and without any support in Congress. In a parliamentary system, such a person could never stay in office as Prime Minister, but Tyler held on for nearly four years until his term ended.