The basics
It's possible that your must / early mead simply doesn't have enough nutrients for the yeast to continue going gangbusters. When I say "nutrients" here, that includes more than just the sugars in the must -- yeast also need other things in their food in order to perform well, things like bio-available nitrogen, vitamins, and the like. When yeast run out of nutrients, they slow down.
Question for you: When you mixed up your must, did you include any yeast nutrients? If so, what kinds, and in what amounts?
Anecdote
In my initial recipes years ago, I used only a teaspoon of Wyeast yeast nutrient and two teaspoons of diammonium phosphate (DAP). Those batches took a while, and I thought that was just the way mead worked. Then I read around a bit, and found out that I could safely add more nutrients to speed things up, so for most of my batches since then, I've tripled the amounts -- one tablespoon of Wyeast yeast nutrient and two tablespoons of DAP.
I have two 5-gallon batches halfway finished right now. Out of curiosity, I decided to try scaling back on the nutrients as part of a controlled experiment in flavor, comparing these two batches (using the same basic clover honey, but each batch with a different yeast, Lalvin K1V-1116 and EC-1118) against my usual results. Both batches went quickly for a few weeks, and then effectively stalled at around a specific gravity (SG) of 1.060 -- but they're still fermenting, just veeeeerrrrrrrry sloooooowwwwwwly (about 0.001 SG points a week). Three months later, after confirming the speed of fermentation, I got impatient, and I just re-racked the one of them and added some yeast energizer to kick it up a notch and (hopefully) finish some time this year.
Possible remedy
If it looks like your yeast have simply run out of everything but the sugars, it might make sense to think about giving them a dose of additional nutrients. From reading a few labels, I've found that products labeled specifically as "yeast energizers" will sometimes mention "stuck fermentation", which is what I've got with my two batches, and what it sounds like you've run into. Have a look at those, read the directions, and let us know if you try any -- and how it turns out.