Ask her "Why do we do this project?" and when she replies that it's unstable and is becoming more unstable just ask again "Is it really?". At that point she will need to think about it clearly and admit that it wouldn't describe the problem correctly. Once she understands that the description isn't accurate you can counter her with a suggestion such as the following:
- The system is no longer supported which increases the risk in case problems occur. The results of which we may or may not be capable of fixing due to having no support for this system.
I can assume that there may be more reasons, but as I read your question, this seems to be the most prevalent one.
It's important to keep asking questions about the PID. The PID is the core document to which nearly every question should be answered in. If the answers are incorrect or inaccurate your project will have a crooked base and may go into a unwanted direction. If you have a good PID, then any questions you may ask should be easy to answer and to defend in case you ask for her to elaborate on it.
If she insists on keeping it as unstable, ask her if the goal of the project is to make the project more stable, rather than more reliable and to reduce risks. If nothing works, ask for a second opinion from someone else in the company. possibly even your manager.
Worst case scenario, she will be as stubborn as an ox and tries to present it towards your manager. At this point it's 100% out of your hands. But I suspect that responsibility for the PID will shift towards you instead if it comes to it.
As a contractor you're hired to show your expertise and are expected to provide results. If you were to accept this PID you would be unable to show either. If in the end the manager still were to agree with her on the PID and the project were to fail due to this. You should have this documented that both she and the manager take responsibility for this part of the PID in case it goes wrong. (risk log entry)