I’ve been wondering this for a while. A lot of stores that sell maple syrup offer bottles made in Maine and Vermont. Why don’t you ever see syrup from NH? I know they have maple trees there.
They’re not part of Big Maple.
Are they sugar maples though? My understanding (limited, I’ll admit) is that while you can get sap from most trees. Sugar maples produce a much higher sugar content and sufficiently to make it commercially viable.
As an aside, I’ve had birch syrup and it is amazing, but expensive because they have to harvest about 10x as much sap to produce the syrup.
The President in The West Wing insisted that New Hampshire maple syrup be served at the White House Pancake Breakfast.
I have some in my refrigerator. My son has a friend who lives in New Hampshire. They make plenty of maple syrup.
I see it whenever I visit NH.
New Hampshire maple syrup doesn’t have the marketing cachet as Vermont maple syrup. So if you’re not in New Hampshire, stores are more likely to stock Vermont syrup, or syrup from Canada with no name.
There’s New York maple syrup,too, but again, you only see it in New York.
I have my daughter bring down some whenever she visits. Upstate NY* (aka Canada) really is good for something. 
*Anything north of Orange and Putnam 
NH makes syrup, but less than 20% of Vermont’s output. Cite.
In New Hampshire you see it all the time.
They’ve put up a couple of (relkatively) new Visitor’s Cenmterrs on either side of Interstate 93 just south of Concord, NH (one on each side). It used to be that these were mainly liquor stores, hoping to sell you cut-rate wine and booze, but they expanded them into full-size rest stops, with one place selling NH products, including maple syrup and stuff made with maple sugar.
You can also get it at places like Polar Caves in NH.
Or over the internet:
You see more “Vermont” syrup because:
*“Vermont * maple syrup in this White House?!”
If you think NH syrup is scarce, try finding *Illinois *maple syrup.
This site claims that 17 states produce maple syrup. Ten states are listed in the wiki article as producing “marketable” amounts of the stuff and Illinois isn’t one of them. As a kid, I’ve been to a sugar bush somewhere vaguely northwestish of Chicago.
I live in Vermont, and last Xmas my MIL gave me a jug of Massachusetts maple syrup. At least it wasn’t from New Hampshire!
I helped out at an Ontario sugarbush for a few springs. We made great syrup. I used to get about a half-gallon a year, at no charge (more if I wanted to pay for it).
When I lived in NY the story was that most of NY’s production was shipped to VT - maybe that’s what happens to NH’s.