Originally Posted by
EI-A330-300
want to book an Y ticket (no checked baggage) and when I select the outbound date, the return shows 4 of 6 returning flights as been "not available" however if I select the fare with checked baggage all return flights are available.
It's very common for an airline to have only a proportion of the seats on a flight available at the cheapest fare and/or for fares to vary for bookings made closer to the intended date of travel. Google "yield management".
How does there system work
As described above.
Anyone able to help
Only with the advice that you've already worked out for yourself - next time, book earlier.