There's a decent chance the BBC will outlast you, especially if you can accept some roughness in the cranks.

In use the balls maintain the surface they roll on, the same way passing trains keep tracks polished despite being out in the weather. Eventually the balls will wear through the hard surface layer of the races and cause them to break down, at which point wear will get much faster.

It's possible that you've reached that point and that's what the mechanic meant by "pitted". So plan on buying a spare soon, just in case, but odds are that even in the worst case, you still have some time.