Not to be supportive of Rahm, but it would seem to me that if one is elected to Congress as a representative of a certain district that one would have to be a resident of that district - whether you own a house there or not you are representing the district.
Then you further take a job on the Staff of the POTUS - after appointment to same. So logic would dictate that you should be able to maintain residency.
After serving 20 years in the military, owning no property in the state I enlisted from, and my parents having moved to another state 2 years after I enlisted I kept my residency in that state.
One seems to be very similar to another.
Not really. Serving in the military or in elected office means you go somewhere different from where you live BY DEFINITION (almost exclusively, though there are exceptions.) Taking a staff position, regardless of who it is for, represents a career move, even if you didn’t intend it to be for more than a period of time. In Congress, you represent your district; in the military, you are representing/defending your country. As a staff member, you represent no one.
Rahm declared himself non-resident, then amended his tax returns after he discovered he was running for mayor. It is not comparable.
He voluntarily forfeited his residency to not pay taxes, then paid back taxes, then claimed he never left.