I have now got to my DAW and have been investigating further.
The Scarbee MM bass manual gives the range of the instrument from B0 to E4. When I enter notes in Sonar in this range it works as expected. Note numbers are confirmed in the event list.
Velocities below 40 play as mutes and 40 and above as sustains. Even at a velocity of 40 the sustain is clearly audible so I doubt if that is causing the problem of non sounding notes, it may however cause things to sound a little different if the MIDI is expecting a smooth velocity curve from 1-127. You may get quiet notes sounding as full volume mutes for example. I think the other Scarbee basses use a similar system but there may be some variations, for example Pre-Bass will sound harmonics for velocities <15.
I don’t think the legato triggered hammer on articulations are relevant to you problem but it’s worth understanding how this works as it may cause bass parts not written specifically for the instrument to sound odd in places.
If you are using Sonar, check the setting for "Base Octave for pitches" in preferences, customisation, display. In my setup this is set to -2 (the default) and with this setting Sonar and Kontakt are using the same convention. If Band in a Box has a similar setting and its set to something different this may be why you think your notes are in range when they are not.
I can't think of anything else I can try without Band in a Box.
edit - MarioD beat me to the Base octave thing while I was typing.