For most commercial carriers the AirlineFlightSchedules query could be used to get more precise information about the flight with only a flight number and approximate times known so long as the anticipated departure time is between the supplied startDate and endDate.
FlightXML requests, like this one, will normally work for up to two weeks of recent history unless otherwise stated.
ident@departuretime found in schedules as the faFlightID in GetHistoricalTrack will allow you to get the results still. There’s no implied limit to how far back this method can search. However, there is also no garuntee a flight in a historical schedule actually occurred. A “flight not found” error may occur in the case of a cancelled flight. This could be checked by providing the same
ident@departuretime to FlightInfoEx so long as the flight is less than two weeks old.