This sounds like a classic hook circuit/FH contacts on an Otis selector. It sounds like your direction setting is common to landing and car. Since you can do this fine from level 5 down, I would be looking at the wiring between 5 and 6(because this is clearly where the breakdown in continuity is happening)and the contacts in this area. Also since the lift goes up form 6 to 7, you can then agree, that the hook circuit in this area is ok, but since it wont go down from 7, it is clear there is a break in the circuit to the down direction set relay.

Look around 5 and 6. Clean all contacts around these floor level relays and let us know how you go.