Sit down with her, make her a cup of tea, and say you need to talk about things.
Tell her that you are worried about September, and you're sure she is too. You know that she's made a good start with her job, but it looks like they're not giving her more hours (this is how ds lost his first job, they just stopped giving him hours and when asked kept saying he was on the books). Be sympathetic. Be kind. Keep your cool even if she is making excuses, just listen and then say "ok, so now we need a plan". Ask her what she needs from you. Offer to help with CVs or driving around to ask in places.
She needs to find a new job.
I know other people may say she's an adult, but adults need to be taught how to find and keep a job too.
The plan is to be on her side, not the grown up telling her what to do, but the adult who can help her get to where she needs to be.
My ds gets very defensive when he feels he's failing. He can assume I'm judging when I offer solutions. It's important I listen to him, and that the solutions come from him, not just me telling him what to do.
Maybe do all this in a cafe with cake to change the scene and stop her from just walking away.
This isn't about nagging or doing it for her, or judging her past behaviour. Start things with a clean slate.
She can do this, you believe in her and know she wants to work, how can you help that happen?
Don't call her work again, it makes her look terrible and will put off her employers from giving her work. Support her by giving her the tools to do these things herself.