Based on the Turkish proverb "Pinch yourself before you punch the other guy" 1
Upset player's perspective
You mentioned that she thinks that particular die roll is a no-win situation for her character. She may be protesting that she is getting robbed of her agency, and being railroaded into your story against her will, and that roll is just there to maintain an illusion of free will.
Re-assess the roll. Is it really fair? Is the target number reasonable for the situation, or did you assign a number based on how much you want her to fail(or succeed)? Be honest to yourself and adjust the roll if necessary.
It may be a good idea to ask her why she refuses to roll but you probably don't want to discuss this during the game. Save that discussion for later, but do ask her for feedback.
If despite your honest introspection, she seems to be the one stalling out of drunken stubbornness, then move onto the next perspective.
Strict GM's perspective
Roll for her and move on. She has no right to stall and ruin the game for everyone. She will probably realize her mistake in a little while and join the game proper.
If she makes a habit out of this despite your warnings, then gradually sideline her character and keep the game going with other players. She may be needing some "alone time" to reflect on the way she plays (or doesn't)
If this habit persists into other sessions, especially when she's sober, she either has the wrong idea about how this game is played and what the rules are (then just tell her the facts out of game), or she is aware and somehow doesn't want to play (it's a voluntary fun activity, one doesn't have to play if she doesn't want to). Figure out the problem and act accordingly.
1: İğneyi kendine, çuvaldızı başkasına. I'm aware that it's not a translation of the original. Just used poetic licence to get the idea across correctly. And it
rhymes alliterates :)