What happened to the East Empire Company?
Solution 1:
There is very little direct lore available on the East Empire Company in Skyrim, or indeed any of the other Elder Scrolls games. However, there are some things we can piece together if we read between the lines.
The EEC was originally commissioned by the Emperor, and is controlled by a council that is appointed by the Emperor. Further, the company's major monopoly is on trade from Vvardenfell. Thus, we can assume that Cyrodil and Morrowind are where EEC presence would be the highest and prosperity would be most visible.
Skyrim is neither of those, and the map of EEC trade routes shows only two major routes impacting Skyrim, while there are many more to other areas of Tamriel. This suggests that Skyrim is simply not that important to the EEC. It's not a hub for the company, in the same way you'll find (in the real world) a lot more US Airways flights out of Philadelphia than you will Seattle, since the latter is a flight hub for the company and former just a port of call.
That said, while there is little specific lore to the effect you're observing, it does seem like a reasonable conclusion that the EEC is suffering a decline in prosperity during the events of Skyrim.
After all, the Great War ended in 4E 175, about 25 years before Skyrim begins. The war itself (though it only lasted four years) likely diminished the EEC somewhat, both due to the general reduction in trade that tends to happen at wartime and the fact that the likely-still-mainly-Imperial guiding council were probably distracted or hamstrung by the events of the war. Further, the eruption of the Red Mountain damaged Morrowind (and it's economy by extension) so much that by 4E 168, it had yet to recover. These events almost certainly contributed to an economic depression within those two provinces that had a correspondingly negative impact on the EEC and any other trade company operating primarily in those provinces.
We only know the major clauses of the White-Gold Concordat, signed at the conclusion of the Great War, since those are the ones that primarily drive the story in Skyrim. However it's reasonable to believe that the minor clauses of the treated included requirements that the Empire pay reparations to the Dominion. It's possible these reparations further damaged (or at least prevented a rapid recovery of) the Imperial economy and thus further damaged the fortunes of the EEC. Note that German reparations for WWI lasted about a decade before being cancelled (and that WWI also lasted four years).
Finally, on top of all that, you have current events: the civil war in Skyrim, which certainly will make the EEC less likely to trade in Windhelm, at least, given that it's a "Stormcloak" city. Orthus Endario's accounts seem to bear this out, as he can be overhead saying:
Windhelm's an easy posting!' they said. Guess they didn't count on Ulfric's little uprising.
and
Can you believe the company won't even dock ships here anymore?
Endario will also talk about pirate harassment of EEC shipments, but I don't think this is a major contribution to the EEC's current fortune as the Dragonborn can be tasked with eliminating the threat with relative ease and the weight of the misfortunes of history are almost certainly more pressing than a little minor piracy.