Just recently my brother's chair went. It was a good ol' boy.
He had it for like 2 years, and then the first wheel broke off. And not just the wheel, the plastic/metal rod holding it in busted, practically no hope of fixing. So he just kept using it.
Then about a month ago he broke a second wheel. And he's a big guy, 6'4", probably 300 pounds or more. He leaned back in it really far, so far that you'd think the chair would bust, he'd fall over, or the backside would snap in half. Very often he did that, and sometimes loud cracks could be heard, though from where on the chair he never knew.
Just a couple days ago I sunk down into it and totally busted off a third wheel, along with maybe ~5 inches of plastic leg. So he had the brilliant idea of just taking the remaining two off completely. Well then something in the center of the plastic limb-star was further down than the wheel-less stubs, so it just pivoted on that central point.
We just trashed it at that point.
Here's to hoping that your chair will fare better!