1. DO NOT touch the truss rod. A lot of myths out there, it only needs to be adjusted if it actually needs it and is very easy to break. That repair costs more than a new guitar.
2. A couple of things come to mind that could be causing this that have already been mentioned. Those need to be checked. Mainly has the string trough in the bridge been cut too deep. Strings can do that on their own by vibration, that's why nuts need to be re cut or replaced after a few years of hard playing.
3. Fret leveling - Already mentioned, is not that hard to do if you have some decent tools. To check it, pull the strings aside and look at the frets underneath. Usually found near the nut where you play a lot of open chords, you'll see little troughs under each string dug into the frets. If you don't see those at the point it's giving you trouble, that's not the problem.
Can be done a couple of ways. A 10 inch or so fine cut file with the tang bent upwards works well, hold it at about a 10 degree angle and run it down the frets. DO not drag the file backward, that dulls it, forward only.
Or, a long, old style wood plane with blade removed, fine grit sandpaper taped to it works very nicely too, it's straight, and heavy enough you don't have to use much pressure, let its own weight do the work. Stop soon as the fret wear disappears.
Then they need to be crowned...that means a hump filed on top of each one. Tedious, time consuming, but that's the way they come from the factory so you have a narrow contact surface.
Truss rod - Puts pressure against the neck to create what is called back bow. A properly adjusted neck should not be perfectly straight, it should have a very slight back bow. In other words, the neck should bow very slightly away from the strings at the middle frets, around where you play a barre E or so. This is a very small difference, but it gives the strings room to vibrate in the middle and not buzz on the frets.
Strings move in a vibrational pattern that looks just like a jump rope. Very little at the nut and bridge and a lot on the middle. We're only talking .015 inch here though, not much...I keep a 2 foot machinist rule for checking it. Long as the neck and straight, if I can slip a business card under it in the middle I leave it alone. If you can slip a credit card under it that's the maximum back bow.
The only time the truss rod should be touched is if it does not have that back bow, or has too much. And it MUST be done right. A drop of oil on the business end, let it sit overnight. (You know what kind of environments guitars go through, do you really think that nut has NO rust????) tightening the nut clockwise bends the neck straighter, and closer to the frets ion the middle, for less back bow. Loosening creates more back bow.
IMPORTANT - one quarter turn maximum, let it sit overnight to settle in. Check it, adjust if necessary, let it sit overnight again. I prefer to let it sit 2 days if possible. Do not get in a hurry. Truss rods break very easily. Just trust me on that one...

Should not be touched unless definitely proven necessary. If you have the least bit of doubt that you can do it properly, take it to a good repair guy. If you screw up, the neck is toasted, the only repair is replacement. Expensive...
Truss rod has nothing to do with action or intonation, as some people will try to tell you. Its only function is to create and adjust back bow, period. That tiny difference will not affect action or intonation, but do check intonation when doing any repairs on a guitar with adjustable bridge. And always check intonation with new strings.
I think there is a possibility the problem you describe could also be caused by something coming loose, my guess would be the glue holding the fret board down could be letting go a tiny bit in that area, or possibly the block at the end of the neck, but I would think it would be all the way across the neck if it were the inside block, not just a couple of strings.
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