Okay, Im used to six string guitars, and them sometimes having issues with fret outs or dead frets. I strung up my Peavey T-20 bass with Rosewood 'fingerboard'( how can you call a fretless a "fretboard"?) , and between the 15th and 17th fret, theres a dead spot where it the notes are dead on the two high strings. I adjusted the micro tilt, and also the trussrod, but havent messed with the saddles mostly cause I can't find a allen wrench that fits which is very odd ...but the saddles seem to be allright, and the action is already fairly high. So, on a six string I would whip out my fret leveling tool and grind away, but what to do on a fretless bass? Do I use the same tool to level the board instead? Would it scratch up the rosewood?
Could it be the strings? I have had that effect from time to time also had it disappear when I got new strings. I am a big fan of DR strings, and I have never noticed that with any of their strings (yet). Just a thought.
Don't go filing away at your fingerboard without any knowledge of how to do so. Are you sure it's a dead spot as in the fundamental decaying faster than the overtones, or do you mean like an uneven spot that is too high and making the note buzz too much?
If the strings are not buzzing or "fretting out" on the fingerboard it may not be a levelling issue. Necks will often have 'dead spots', or areas of the fingerboard where the sustain is much weaker than elsewhere on the board. The effect is usually more noticeable on basses than guitars and it's often most obvious on the G string. It's very common on Fender-style basses in the 5-8th fret region. It's very common on bolt-on necks, but set necks have it, too. There are a lot of theories about why it occurs, but it's often lessened by adding carbon fiber rods in a neck's construction, adding mass to the headstock or experimenting with strings that 'get along' with that particular bass better. The answer to your question about fingerboard levelling is pretty simple - just use a straightedge right against the wood and parallel to the strings, but unless your truss rod is very mis-adjusted, I doubt the fingerboard itself is the source of your trouble.
I have a good machined straightedge that works great for levelling high frets on six strings. No, maybe "dead spot" isnt the right word, its not just lack of sustain or a buzz, its a totally dead note -just wont produce a legitimate note at all, just a dead spot like high fret on a six string.
You could lay a white sheet of paper on a table top and lay the straightedge along the fingerboard while holding the bass in playing position. Look for the white background showing through between the straightedge and the board. You should see a little bit of relief, but it should be uniform and it should be centered closer to the nut end of the neck. If you see a hump or a rise anywhere near your trouble area, then you do, in fact, need to level the board. If not, then it's just you friendly neighborhood dead spot.
I have a G&L L2000 fretless that had a lot of dead spots that weren't noticeable with rounds on it (when I bought it) but with Chromes, they were everywhere. I took it to the corner repair shop that I'm blessed to live less than a mile from, and they explained how neck angle can adversely affect the whole geometry of an instrument, that's why the neck angle screw is there, blah blah... They called later and said the fingerboard had a bump in it, $75 to level it. It plays like a charm, no dead spots.
From your description, it sounds like you have a slight bump in the fingerboard surface. While a larger bump or dip will cause an ugly buzz, a small one can make the notes die out like that. It's as if you were holding the string down with your ring finger, and then very gently touched the string with your pinky. The contact point is close enough that you don't get the buzz, but enough that it shuts the string down. No big deal. It just needs a light resurfacing. Use a flat bottom hardwood block about 8" long and 400 grit stearated paper (the gold stuff). Work in gentle strokes right along the path of the string, rolling it slightly to follow the fingerboard radius. You'll be able to see the high spots and low spots by the abrasion marks. Take off just enough to get a uniform scratch pattern along the path under the string. When it looks good, polish it up with gray Scotchbrite on the wood block, followed by white Scotchbrite without the block That will bring the surface back up to a gloss. Then give it a fresh coat of something like Stew-Mac's fingerboard oil to protect the wood. In my shop, it would be a 20 minute job. Note: Like the others have said, most basses have some dead spot problems caused by structural resonance, and that can't be solved with the fingerboard. But what you are describing sounds to me like a small fingerboard lump. Fix that first, then try it.