Not necessarily; we've recently found some routes where goods were
discovered during the game, but one end of the route still exists
long after the expiration date. In at least one case, a city is still
purchasing a good more than 50 turns after it was first sold, and it
has long since disappeared from the selling city. In another case,
a trade good is still being sold, but the buying city stopped buying
it many turns ago.
Maybe these will just go away over time (but more time than stated
in the rules); guess we'll just have to wait and see. The first case
is more worrisome, since goods that never drop from a buying market
when they _do_ drop from the selling market will eventually eliminate
trade within the game. Markets that never stop selling a good are less
of a problem; you just need to find another market if the first one stops
buying it.