This is a story that I read sometime in the late 1980s or early 1990s. The story takes place in a distant future on Earth, after the crash of a high-technology civilization (presumably our own) whose very durable artifacts and ruins are still everywhere. It follows two travelers, a male and female (not quite sure they were both fully human), who are on a quest to find an "oracle," which the story mentions was originally a weather-prediction computer in ancient times. (I think it's explained briefly that its non-linear logic circuits, necessary for weather prediction, give it unique predictive abilities.)
The journey takes the pair to a road built by the Ancients that leads up into the sky. Notably, the road has no visible support -- it just kind of hangs there, going up and up beyond the clouds. They travel up the road for some time, facing hazards like storms and sections where the road is partially-collapsed. Along the way, they start to fall in love.
They eventually do find the computer, and are given the chance to ask it questions. (Maybe the limit is one question each?) One of the pair (call him or her A) gets a prediction along the lines of: "A will love B for the rest of his/her life. B will love A for the next 27 minutes."
Shortly after, one of the pair dies (falls off the road somehow, I think). If I'm remembering correctly, the surprise ending is that it was A that died, implying that B basically forgets all about A quite quickly. (My original expectation was that B would die, leaving A pining.)