How much will a power outage
affect your incubator? Is it worth keeping the eggs going after
the juice comes back on, or should you pull the plug and start over?
We had a two to three
hour loss of power during the second week our incubator was running,
and we did see a slightly lower hatch rate, but not enough that I feel
we should have just started over. During our first hatch of the
season (same incubator, same parents), we had 90% viable eggs, 95%
hatch rate of those viable eggs, and a 94% survival rate to four
weeks. In contrast, the set of eggs that lived through the outage
had 95% viability, 80% 
hatch rate, and 94% survival
(to one week). (See my 99 cent ebook, Permaculture
Chicken: Incubation Handbook for more information on
calculating these rates and improving your hatch.)
How long eggs can
survive in the incubator without power depends on a variety of
factors. Length of time the power is out is an obvious one, and
so is air temperature in the room --- shorter outages and warmer rooms
cause less of an impact. If you're around during the outage (we
weren't), you can close all the vents, add a hot water bottle if you
have one, and wrap the incubator up in a 
blanket to conserve heat,
which will mitigate the outage to some extent.
Another factor to
consider is age of the eggs. The further along your chicks are in
their development, the less likely they will be negatively affected by
a power outage. As embryos develop, they begin to produce a bit
of heat by themselves, which warms the inside of the incubator slightly.
Have you left the
incubator running after a power outage? I'd be curious to hear
how 
long your power was out and
what percent of the eggs survived to hatch.
Our chicken waterer got the surviving chicks off
to a healthy start with clean water.
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Heath --- Our Brinsea Octagon Advance doesn't have that feature --- I wonder what kind of Brinsea Advanced incubator you have? How long does their cool down period last?
I've read varying reports on whether the cool down cycle every day helps or hurts or does nothing. You'd think we'd be able to scientifically prove it one way or the other, so it's odd that I see so much conflicting advice.
We have the Mini Advanced model that will do 7 egg and turns the eggs. The manual has a chart for setting your cool down period by the type of egg you're trying to hatch. Our duck eggs call for 180 minute cool down period.
They have a PDF available at http://www.brinsea.com/pdffiles/MiniAdvancePlusUS.pdf
Thanks for the followup! I've excerpted the relevant passage below:
Bird breeders have known for many decades that eggs can be cooled for limited periods of time during incubation without causing problems but recent research has shown that hatch rates can increase significantly as a result of cooling. This research was carried out with poultry but it is generally accepted that the benefits can apply to waterfowl too. Cooling is an entirely natural process as most birds will get off the nest at least once a day and leave the eggs unheated for a significant time. From Brinsea’s 35 year experience, the best hatch rates are always achieved when the incubator can best mimic the natural nest conditions.
The precise details of which days and what cooling period each day should be used for best effect are not known but Brinsea have assessed the available research and recommend the following daily cooling periods from day 7 through to 2 days before they are due to hatch (the same point that automatic turning would normally be stopped). Smaller poultry, waterfowl and game bird eggs: 2 hours each day Larger species eggs (e.g. duck and goose): 3 hours each day
My analysis is that it sounds like they don't have any data. But the 2 hour figure does seem to suggest that a short power outage should be no problem.
Anna, I thought you might be interested to hear our ducks in that incubator have begun hatching. So far two have hatched and all of the others have begun to peck their way out.
http://www.youtube.com/watch?v=KsnCnqyMLvg