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I am not a veterinarian, but my guess would be that if humans can get sleep
apnea, why not cats? The problem is that in humans, this condition is
generally treated with a CPAP machine. Now, just try to convince Fluffy that
he needs to wear this contraption:

http://www.aftonmedical.com/cpap.h1.jpg

Another way to treat sleep apnea in humans is with weight loss. I don't know
if your kitty is overweight.

Sometimes, humans are also treated with special dental appliances, called
"mouth guards" (Here is a link to an image of a human mouth guard called
"the Silencer."  I don't think you're going to convince Fluffy that he needs
to wear one of these deals, even if a cat dentist would take an impression
of his teeth and custom-make one for him):

http://www.the-silencer.com/images/pro1.jpg

One of my extended families members has chronic atrial fibrillation (heart
is not in proper cardiac rhythm and heart valves sometimes flutter) and
sleep apnea. She is overweight and refuses to wear a CPAP. The doctor has
stated that he will not be able to keep her heart in regular rhythm (it goes
in and out of atrial fib) unless she simultaneously treats her sleep apnea.
Despite the fact that she has untreated sleep apnea, you should know that
her atrial fibrillation fortunately has NOT progressed in several years. Of
course, it would be better if she would agree to use the CPAP, and then the
doctor could cardiovert her back to normal rhythm (and have a good chance of
keeping it there!), but that's not going to happen any time soon. She has
probably had this for condition for years. She is 83 years old and is still
going strong.

It will be very interesting to hear what your vet has to say about this, so
please post back after your appointment.
Best regards,
---Cindy S.

I'ved noticed my cat doing this sometimes. I think it is just a stage in
their sleep when they breath too shallow to see. The fun part is when they
start dreaming where they shutter, twitch and even meow.
John