> My question is whether apistan strips can be left in
> the hive over the winter

I'd say "no".

The label also says "no".

George Imrie would say "NO!!!!!", and you would need the
services of a skilled surgeon to have your eardrums repaired.
(Let's all hope that George regains his voice quickly, or I'll
have to drive up to MD and wire a 2000-watt PA system to
the battery of his scooter.  Hey George - 6 Volt or 12 Volt??)

I don't know of anyone who would say "yes".

> My understanding is that varroa mites build intolerance to apistan
> through genetic mutations that would occur only when the queen
> is laying eggs and not during the cold winter months

But the queen starts laying much earlier than you might suspect,
and the product is designed to be used for a specific limited period
when the weather is warm enough to let the chemical have some effect.

Yes, your reasoning is very sound, but if beekeepers won't follow the
label instructions on a pesticide, we can't expect anyone else to do so.

        jim