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I assume that your wife isn't a national of an Annex II country such as Canada or Japan; if she is then she doesn't need a visa in any event.
So, I'm thinking that as long as we haven't been outside of Italy for more than 6 months (and as long as we return to Italy once every 6 months), the residence card should still be valid, and we should thus be able to continue using it.
But your absence isn't temporary. You have relocated. You no longer reside in Italy.
But EU law does not specify when a residence permit (or a residence card issued under free movement law) becomes invalid. It only establishes limits within which national law must operate. So Italy can provide that the Italian residence card becomes invalid under whatever conditions it chooses, as long as those conditions comply with the directive. In particular, any automatic loss of validity because of absence must comply with article 11 -- the provision can be more generous, but it cannot be less generous.
But really, you should not worry about what any authorities make of the card, because Article 5(4) of the directive provides
Where a Union citizen, or a family member who is not a national of a Member State, does not have the necessary travel documents or, if required, the necessary visas, the Member State concerned shall, before turning them back, give such persons every reasonable opportunity to obtain the necessary documents or have them brought to them within a reasonable period of time or to corroborate or prove by other means that they are covered by the right of free movement and residence.
In practice, this means that if the two of you can get to the passport inspector and prove that you are married and that one of you is an EU citizen, the other should be given a visa at the border, if one is required (in practice, this seems to boil down to being admitted without a visa, because the visa is needed for entry -- under article 5. There's no need to have a visa during the visit.
So all you need to worry about is the airline. Will the airline be able to see that the residence card was cancelled (if it has been)? I suppose not.
But the consequences of being wrong about that are fairly severe, and the cost of protecting against that possibility is the time and effort of getting a free visa. I'd only risk traveling with the residence card if I were unable to get the visa for some reason or if getting the visa presented a significant difficulty.