*A Hub: Dulles is a hub for Star Alliance which is an airline alliance with United, Lufthansa, Swiss, etc.

TATL: Trans Atlantic Flights.

To answer your original question, its hard to tell whether flights will drop, but hopefully you are expanding your google searches to all airlines and not just United. Unfortunately, it might involve making a connection in the US and/or Europe to get to your final destination.

Easy for a solo passenger. Tougher for a family.

Another option is looking at other airports in the region. They might have lower prices (especially the New York airports as they have more competition).

Also, look for other destinations in Europe like main hubs and then take cheaper flights from there to ATH.

But I think the demand is going to be strong for TATL flights, so I don't see prices coming down anytime soon.

But keep searching. Good Luck.