I had a bath fan mounted to a attic vent (the 12" square kind
with the 6" hole). THis worked for several years but then I
found that I burned out the fan motor. I replaced the fan motor and
after a few years burned that one out as well.

I investigated the whole system and found that the attic vent had a
screen inside it that is used to keep the bugs etc out. Over the
years this screen became clogged with lint etc from the bathroom. So
the fan motor was working extra hard to push the air through the
clogged screen. I also found that the flex duct pipe that I had
going from the bath fan to the attic vent did not have insulation etc
on it so the moist air would condensate in the duct and actually run
back into the fan and eventually dripping on the bathroom floor.

I just replaced the whole system with a direct line over the attic to
the soffit area with a vent port out of the soffit. This duct is
insulated and is only about 5 ft long (while the old system - duct
was approx 12ft long) I purchased the vent port from a friend that
does HVAC work. It made specifically for venting fans in soffits and
actually "twirls" the air as it leaves the port (grill).
This twirl effect causes the air to be directed out away from the
house.

I think this system will work much better than the original
-shorter pipe
-no screen in the system to clog up
-no vent on the roof (got covered in the winter with snow)
-the vent port is close to a outside deck so I can keep an eye on it.