Canonically, it becomes Indefinite for those purposes. A fairly common house rule I've heard is for it to be fixed as it was at the point where you start labwork. I think it's a limitation of the simplistic system - ideally you'd want ratings for how quickly a thing degrades vs how strong it is - ie. Blood is very strong, but rapidly weakens as it dries, dried blood is rather weak, but still better than a footprint. That complicates matters though.
If one spends a whole season fixing the conenction and a pawn of vis I think that is entirely fitting that it be an indefinite connection. Anything less (and in the opinion of some even this) would be a waste of a season.
I have to say an entire season seems rather too long anyway. I allow 1 month (but then I do experience in months). It has only been done once, so far, anyway. I also allow a mage's casting sigil in some circumstances to be an arcane connection, and therefore to be fixable also. We have a crow that was enchanted (and therefore had a more than instantaneous sigil) that was fixed. However, there needs to be a spell against putrefaction cast each moon to stop it from rotting as the fixed thing is the sigil, not the bird.
In a different solution, my troupe has ruled on occasion that a number of arcane connections equal to the magus' magic theory score can be fixed during a season - but in this case while they are permanent they are only as strong as they were when the process started.
I'd allow multiple lab activities to cover fixing ACs... Which would allow for up to 2x magic theory (as that is the max vis you can use...)
I am also in favor of the permanent penetration modifiers - after all, they are permanent ACs - and that is one of the very few ways to get a permanent AC...
The original multiplier. Just because you just made it useful everafter shouldnt increase how GOOD the connection is.
According to the RAW the Penetration modifier depends on how long the Arcane Connection lasts for. How long the Arcane Connection lasts for is how good it is. Longer duration = better Arcane Connection.
An Arcane Connection with an indefinite duration has a Penetration Modifier of +4. An Arcane Connection that is fixed in the laboratory is explicitly listed as an example of an Arcane Connection with an indefinite duration.
There is no real room for ambiguity in the RAW. Of course, you can obviously house-rule otherwise if you wish.