If your MM is embedding itself into the wood - lighten your touch! A set of MM lasts me for years. When you are sanding with MM, it should never get more than slightly warm.
Wet or dry, your MM should last through many, many uses.
I have gone through a few sets now...always wet sanding. I got about 80 pens or so out of the first set but they were working very poorly for quite awhile at that point. After being reminded of how much better a new set works, I wanted to replace the next set after maybe 35-40 pens. Now I have switched away from MM and find finishing to be quicker without them and the results just as good in my opinion. This way I can replace my sandpaper every 4-5 pens so it's always fresh.
With the MM I had to pre-sand with 400 grit paper and then use all the colored pads, then polish with HUT and buff after. Now I just sand with wet/dry paper in 400,600,1000 & 1500 grit, then HUT and buff. That's a lot less sanding steps. I find the MM scratches are harder to get rid of than the regular sandpaper scratches and I also had to go back and repeat grits more often with the MM pads.
I am happy to not be using them now
Just my .02