How did a 90-day Mars rover keep rolling for 14 years?

Because it managed its energy as carefully as a household budget. Opportunity went to Mars with a planned 90-sol mission, and it was operational for 5,111 sols, 14 years and 138 Earth days: 57 times its designed lifespan. The reason was careful operation: it kept recharging its batteries with solar power, and it hibernated during events such as dust storms to save power.

The arithmetic of its energy is what governed its life. Its solar arrays generated about 140 watts for up to fourteen hours per sol, and lithium-ion batteries stored energy for the night. At the start the panels could provide up to about 900 watt-hours a day, but in its first Martian winter that dropped to under 300 for two months, and global dust storms in 2007 cut power so much that it, and its twin Spirit, could only run for a few minutes each day. By 2016 Opportunity had endured seven Martian winters.

In the end it was dust that decided. In early June 2018 a planetary-scale dust storm developed, and within a few days the solar panels were not generating enough power to maintain communications; the last contact was on 10 June. The final transmission recorded 22 watt-hours for the sol and the highest atmospheric opacity ever measured on Mars. After over 1,000 signals went unanswered, NASA declared the mission complete on 13 February 2019.

A journalist's translation of the last data, "My battery is low and it's getting dark", struck a chord with the public, though it was his rendering of the data, not words the rover wrote.