France. I know, I know, no one likes the French, but French naval and
military intervention kept the (soon to be) Americans going. British
navy had a pretty good blockade going, but with the arrival of the
French, Britain was no longer dealing with just a colonial navy.
Shipping could get through and the trans-Atlantic trade (a key
element in American wealth) could continue. In addition, there was a
very real possibility that this little rebellion could escalate into another
France/Britain slugfest if it continued any longer. Which happened
anyways in a few years. So, that along with all the other reasons
mentioned (logistics and American tactics are big ones), Britain
pulled out.

As for the American commanders...well, they weren't that great. On
the whole, they were so-so at best. Most of the British generals
were better tacticians (of the "line up and fire" style of war), but either
they were more interested in living it up in the colonies, or couldn't
adjust to the terrain and "ungentlemenly" tactics of the Americans.

ak"new to this board so...Hey Everyone!"scully

P.S. Oh, almost forgot. The British people themselves weren't
wildly for the war. There were a considerable number of people
who just wanted to let the colonies go if they were going to be so
much trouble. So, not much support on the home front was also a
factor.