LONDON — From the start, Irish voters were less beguiled than the rest of the world by the novelty of having a young, openly gay, half-Indian man lead their government. Now, as they go to the polls on Saturday, these voters are poised to turn their trail-blazing prime minister, Leo Varadkar, out of power.

As was the case when Mr. Varadkar rose to be prime minister, or taoiseach, in June 2017, his declining political fortunes have had relatively little to do with his ethnicity or sexual identity. He leads a party, Fine Gael, that has been in power since 2011, and with voters frustrated over Ireland’s housing crisis, Mr. Varadkar, 41, is facing every politician’s curse of being a status quo figure in a change election.

That has outweighed the credit he got for his sure-footed performance in negotiating with Prime Minister Boris Johnson over the status of Northern Ireland after Brexit. Mr. Varadkar was able to extract a deal that avoided a hard border between the Irish Republic and Northern Ireland by aligning the north with the European Union more closely than the rest of the United Kingdom.