Well, several things.
First thing I'd check is the G# hold down. If you're talking about a modern horn, everything below D will want to lift the G# pad unless that hold-down is just right. And if you screw the screw in even the tiniest bit too far, now the bell key pads won't close.
Another factor here is that the surface on which the little cork-tipped screws bear is almost never perfectly flat and perpendicular to the axis of the screw, so the cork deforms into a tilted or cupped shape. Then when you turn the screw, the edge of that cork is what's pressing, not the entire surface, and it deforms quickly due to high load. So it might look fine for 10 minutes and then it's deformed enough not to be doing its job. The long term cure is either to modify that mating surface so it's flat; perpendicular to the axis of the screw; and large enough that none of the cork hangs off the edge - or, to put a flat-tipped screw and move the cushioning material to the key cup. (Which is usually what the adjusting screw bears on.)
Next thing is the low C# hold down. As Stephen points out, it's kind of a bogus mechanism, and I won't get into the details, but you'll probably have to adjust it so that it allows the C# to crack open ever so slightly when playing B, just to keep it from holding the B open. However, misadjustment of the C# hold down won't affect low C# or low C.
Third thing is leaks up high on the horn. Just because the higher notes play fine doesn't preclude a leak up there acting as an unwanted octave vent for bell key notes.
Next would be tenon fit (wrap the joint with electrical tape and see if the problem goes away) or bell/bow joint leak (wrap the joint with electrical tape and see if the problem goes away).
Lastly would be a crack in the actual material of the horn itself. I have a bass sax with a stress crack in the loop area; by the time I found it I was tired, so I just patched it with some aluminum tape and it's still holding 10 years later.
I'm going to bet on the G# holddown from the description - everything plays fine down to D then goes out the window with low C# and below.