In this case ずっと means "Forever/All the time", not "Always".
Always means that it's always the case when certain conditions are met. Unlike "All the time / Forever" it doesn't mean always for a long time. For example, "When I order something at a restaurant, I always ask for a hamburger." it doesn't mean that I always ask for a hamburger, but it means that it happens only when I go to a restaurant and order it, which is a specific condition.
Forever/All the time means that it's always the case, regardless of the conditions, from a certain point in time, for a long and continuous period of time. For example, "That ball has been there since 3 years ago." referring to the state of being there continuously from the beginning, 3 years ago, to today. It's also used in the sense of eternity, sometimes referring to the future, as in "Let's be friends forever."
So, in this case, they don't have any conditions to be いつも(Always), so that's why the original sentence is ずっとって訳にはいかない - It can't be forever.
I hope this could makes sense the usage of "訳にはいかない", ask me in the comment if you got further question