I saw on Orbitz today (click here) that Alitalia may cancel flights due to fuel shortages as well as other problems that they are currently experiencing. Alitalia is currently in talks with its unions to keep the airline going while it restructures. There are talks of Lufthansa being a possible partner to Alitalia.
On the Alitalia web site (American side), they claim that they will keep their flights scheduled (read their notice here). Since international flights are more profitable than the shorter domestic ones, one can surmise (and, please don’t quote me on this!) that they will make every effort to keep their international flights running.
If you do have a reservation on Alitalia in the next few weeks and months, please pay careful attention to the news. It might be wise to reconfirm your flight to make sure that everything is on order.