There's more than enough discussions about how avoiding the ambush in Teutoburg Forest and crushing Arminius isn't going to cement Roman rule in Germania.There's also the problem that no empire lasts forever.
That why I said butterflies. It would be impossible to predict what would happen four hundred years after such a momentous event, but I don't think that Rome holding it and Rome lasting is 100% ASB.
I think that avoiding the Varian disaster is enough to cement Roman rule west of the Elbe. I've read arguments on both sides on this site, but I'm more convinced that avoiding the disaster, Rome could possibly held the province.
Not 100% guaranteed, but say, 60-70% sure that Rome is gonna hold it till it falls.
Now as for no empire lasting forever, that is mostly true, but it does not mean that it couldn't happen, or it couldn't reform after it fell. I see the series of events in the 5th century that lead to the dissolution of the WRE is simply due to a series of bad luck and bad breaks, and with a little more luck, the WRE could have weathered the storm.
Having the Elbe as the boundary would cause so many ripples and so many changes that it would be futile to speculate on what would happen five hundred years down the road. It could lead to Rome collapsing faster, it could lead to Rome collapsing later, or it could lead to Rome lasting till this day.
In this post, I'm answering the AHC by positing the last possibility.
The battle of Teutoborg leading to the permanent province of Germania, may lead to butterflies that lead to a lasting Roman Empire.