This is an idiom for a disastrous loss or collapse. As the American Heritage Idioms Dictionary has it (via Reference.com):
(the) bottom drops out
Also, the bottom falls out. A collapse occurs, as in The bottom dropped out of the steel market, or When they lost the game, the bottom fell out of their hopes to make the playoffs. This term alludes to collapsing deeper than the very lowest point, or bottom. [First half of 1600s]
A very similar expression is for something to fall through the floor, similarly indicating a breach of what was previously thought to be the worst something could be.
The quoted text, therefore, is alluding to a dramatic decline in the condition of the European economy in the 14th century. Coming as it did indicates that the timing of it is significant— in other words, the closing of Europe's overland trade routes with Asia occurring at the same time the European economy was in poor condition made the pursuit of seaborne trade all the more important.