are Subarus with replaced head gaskets permanently fixed?

NO- with this red flag, why would you consider these cars at all?

Ask to see the recipt for the work.If the heads were milled or replaced,and the job done at a reputable shop,you shouldnt have to worry about it.Quality replacement gaskets are an updated design

Head gaskets, rust, oil consumption are all issues that Subarus of some years have been plagued with. If you get one that is repaired properly it should run a good long time. Perhaps consider in addition to Subaru, the Infiniti G37X AWD. We had a 2009 model and it was great, purchased it new and after 6 years not a single trip to the dealership.

No car has permanent head gaskets. If they used proper multi-layer head gaskets and did a good installation job they should last for a very long time.

A better gasket that reduces squiggle between the heads and block in the 2.5i was introduced in 2010, solving this endemic problem. No other iterations suffer. Bob, I agree that the G37x is such a great vehicle that I refer to our '13 xS as the "SuperSubaru". Yet despite adding the G37 Coupe's fatter rear swaybar (just do it!) and mixing staggered wheels and UHP tires I can't get the turn-in to be as clean as my Subies. But the linear power delivery and ultra-reliability is legendary...real A4/3Series killer. When clients suggest that they need more power than the '13+ FB 2.5i I simply suggest they get pony up for an off-lease G37x instead of Subaru's 6 cyl. Apples and oranges in use of aluminum and build quality. Too bad the Q isn't as good....

Agreed, not sure what happened with the "Q", it should have been better.