If your strings are too high above the frets this can make it harder to fret cleanly. Stick dulcimers should conform to the same set up parameters as lap dulcimers, guitars etc. If the strings are too high, you have to press harder to get clean notes on any stringed instrument, except those played with a slide or bar, such as steel guitars. Do you have a friend who plays any stringed instrument? Perhaps they could look at the action and see that it is set up correctly. If not, a good rule of thumb for diatonic instruments is the string should be no higher above the first fret than the thickness of a dime placed on the fret board behind the 1st fret, and the thickness of a nickle placed on the seventh fret. If the strings are significantly higher, the height needs to be adjusted.
Another possibility is that another finger is leaning over and damping the string, making it thud. Make sure the end of your finger is pressing the string, not the side of your finger. This is less likely on lap dulcimers because the hand is not around the neck of the instrument. It's more common on neck type instruments. Don't let the neck of your strum stick fall into the V between your thumb and index finger. The pad of your thumb should be placed behind the neck, allowing you to oppose the downward pressure of the fingers with upward thumb pressure. An observer facing you should not be able to see any part of the last joint of your thumb. This is a pretty common problem, work hard to ensure you don't have this problem. Unlearning a bad habit is REALLY HARD! I still catch myself doing this after all these years playing guitar, etc.
If you had a high fret, a buzz or rattle would be more likely to happen, rather than a thud. The rattle would occur at one or more frets below the high fret. A thud indicates the string is probably not touching the fret at all.
Paul