Then you are using the wrong alcohol stove. This is a common mistake - people think that an alcohol stove is an alcohol stove, but there are many, many kinds, and some of them work for some purposes better than others.

I've used mine below freezing, high elevations, all seasons, for cooking as well as boiling water, and while at times I have failed to prime correctly I can honestly say that there is really no limitation for them.

I have two stoves that take longer than six minutes to boil - they are used for simmering or cooking. I won't pretend that alcohol stoves are the fastest stove around but there are stoves that will boil in less than five minutes. My cat can stove consistently clocks at 4 minutes.