In 2011, she took 50 per cent of the vote over three rivals, winning 51 of 59 of the eastern Arctic's polls.
Since then, she can point to a number of accomplishments, including hundreds of millions of federal dollars for much-needed housing and favourable treatment for Inuit organizations seeking federal infrastructure money.
The territorial government's request for greater borrowing powers was granted. The North now has its own economic development agency, spreading federal dollars throughout the region.
Aglukkaq is a voice from the Arctic around the cabinet table where the big decisions are made.
And yet, some have doubts.
"I know that there's a lot of disappointment with our current MP," said Madeleine Redfern, former mayor of Iqaluit and now head of the Ajungi Group consultancy. "There's a lot more negative feelings toward the Harper government."
Pleasing Inuit elites in the territorial government and land-claim organizations doesn't necessarily produce popular support, said Jim Bell, longtime editor of the Iqaluit-based Nunatsiaq News.
"If you are an office-holder or political leader in Nunavut, you're probably going to be at least mildly satisfied. (But) Inuit corporations are not necessarily in touch with the grassroots."
Ottawa's program to subsidize Nunavut's notoriously high grocery costs is widely disliked, said Bell.
"Whether it's fair or unfair, everyone in Nunavut who is unhappy about food prices is also unhappy with Leona."
Aglukkaq also faces backlash over her perceived failure to back a wide coalition of Nunavut mayors, hunters, trappers and Inuit wildlife regulators opposed to seismic testing off the coast of Baffin Island. She must deal with a growing sense that she represents Ottawa to the people of Nunavut, instead of the other way around, said Redfern.
The minister recently came through with an long-awaited announcement on a deep-water port for Iqaluit and money has been available for small, short-term projects such as community playgrounds. But other projects — harbour facilities in the rest of Nunavut's communities, a road into the central region, better broadband access — have gone nowhere.
"A lot of these announcements are based on Ottawa's priorities, not on our communities," Redfern said.
Liberal candidate Hunter Tootoo may take her task on that. A former member of the territorial legislature, Tootoo was most recently head of the Nunavut Planning Commission, a group that has opposed Ottawa's pro-development agenda.
The New Democrats had yet to nominate a candidate in the early days of the campaign after Jerry Natanine, mayor of Clyde River, withdrew his bid.
Still, an incumbent has an edge in this far-flung riding where votes are decided more on the candidate than party platforms or leadership debates. Aglukkaq has visited most of the riding's communities — no small feat in a constituency spread over three time zones.
"It took me three years to get to every community," said Nancy Karetak-Lindell, who held the seat for the Liberals before Aglukkaq won. "Getting people that are well known in their community or region to endorse you was a way to get known. That still works today."
Personal loyalties count, said Bell, but Nunavut politics increasingly resembles that in the rest of Canada, with dividing lines between left and right playing out through issues such as development and social spending.
And social media are helping shorten some of the distances, said Karetak-Lindell.
Still, she said, it's the candidate that matters in the North.
"This is why I come down again to personally getting to know people. I think that's a key factor in our territory."
Also on HuffPost