**Asymptotic**(adjective)

**Getting ever closer to something but never actually reaching it.**

This is a mathematical term relating to a curve approaching a straight line on a graph. But I think it could be useful in a wider, non-technical sense too, as there does not seem to be any other way of expressing the general idea so concisely.

"The explorers' advance toward the South Pole, ten miles away, was brave but asymptotic. Four miles one day, then two, then one, then a half, until they eventually gave up."

"He is making asymptotic progress on his novel. I don't think he'll ever finish it."