I'm not on my computer with Storyline, so I can't look at your file. But I think I can answer your question anyway.
I assume you have a trigger to disable or hide the Next button when the timeline starts. As you discovered, that simple trigger will run every time the user visits the slide.
To prevent that, add a condition to the trigger so it will only run the first time the user visits the slide. A condition could based on buttons on the slide being Visited, layers being viewed, or even a variable that's changed on another slide.
In your case, use a condition that checks the value of the text-entry variable. Because you want Next disabled when the password hasn't been entered yet, the condition would be "if [text-entry variable] = blank."
The variable won't be blank after the user enters the password. Thus, the condition won't be met when they return to the slide, and the Next button will remain enabled.
You can find more info about trigger conditions here: Storyline 360: Working with Triggers | Articulate - Community
And here's info about different ways to control the Next button: TIP: Controlling the NEXT Button 101 | Articulate - Community
