This is totally random, but I have personally seen it, so worth a shot. I'm throwing this out there, because I am not sure what you mean by:
loses power and nearly stops cutting
is it bogging out, or throttling down?
If it is bogging out, your rakers could be filed down too much. When you are cutting on other parts of the bar, the saw will force itself out of the cut and keep the RPM's up. But when you cut on the bottom near the saw, the saw dawgs in and it cannot back itself out of the cut and it is trying to take too much of a bite for the saw.
If it is throttling down, you may a fuel line issue. Your saw digs in the most when cutting on the bottom near the saw. It will suck the most fuel at this point, if your filter or line is partially clogged, your saw could be shorting itself on fuel supply. It can also be, as previously posted, the muffler screen.