I was so hoping to find a sticky post in this section with a super easy explanation of how to tell blender to make a seamless fire simulation.
The guys who created the fire simulator are very clever indeed , it looks great!
Im not sure how difficult it is to actually write a seamless simulation with a given time frame - perhaps its rocket science deluxe and will never happen … but it would be cool.
I cant see any way to even bother trying to manually patch it … it will take ages and will never be as good as if it was done via formulation.
sigh…
The problem with creating a looping animation using only physics is that the time scale for physics is linear and fixed, while a loop “curves” back on itself, like going backward to an earlier point in time. Since each frame of physics-driven fire is calculated from a preceding frame, there is no way to set a “target” of parameters for the physics to end up with, which would be needed to have the fire physics end up with the same values as it started with. This is also true of Cloth, Hair and Soft-body physics. In those cases the cached values need to be converted to mesh properties (such as shape keys for Cloth) that can be manipulated over time in a non-linear fashion. I don’t know if the fire sim allows this kind of conversion.
Depending on how it’s being used, it might be possible to fake a looping fire effect by using a compositing trick or two (or three, or six 
). This would use pre-rendered images, which can be manipulated in a time-independent fashion, and given fire’s rather chaotic nature, it shouldn’t be too hard to do effectively. But how you want to use it is a principal determining factor – context is king.