She escaped into cyberspace
Shibata sometimes appears in the last section Mission 3, Gravity Zero. To rescue her, you'll need to have two ID cards from the previous section.
Before you enter gate B03, you can either pick up ID cards off the floor or get them by rescuing survivors. You need one card to open the door that leads to gate B03, but there should be at least two more available.
After you enter the gate, you'll find yourself in a zero-gravity section. Once you've completed that and are back on solid ground, you can use your extra ID cards to activate switches B and C shown on the map (this comes from the Japanese strategy guide - check out the scans of the other pages here).
If Shibata is going to appear, she'll be in the location marked as 1 on the map. She doesn't always show up, however. You can use one of these passwords to find her:
Shibata's rescue is weird! She is one of the few survivors to get her own sequence with special voice acting. When you approach her with Shou, she tells him that she wants to continue sleeping. He reminds her that she has a deadline to meet before transporting her (video).
When Tillis starts to transport her, she disappears and then Chris says "I'm losing her!" Shibata's voice then comes over the intercom saying "I'm free! I'm free!" The sequence ends with Chris explaining "She escaped into cyberspace." (video)
The Japanese versions of the rescue are similarly strange. Shibata tells Shou that she hates deadlines, and he replies that she still has work to do. After Tillis transports her, Chris comments that she ought to grow up, and Shibata giggles.
Shibata sends along one e-mail after being rescued. Like some of the other special survivors, it comes with some artwork:
In the Japanese version of the game, her message says something like:
Dear Burning Rangers, thanks for your help.
My manuscript was reduced to ash, but I'm totally fine.
My editor is also ashen, but I'm totally fine with that too.
I'm going back to the drawing board after all that's happened.
Deadlines are just a gift from your editor to remind you what hate is.
I'll run away properly next time and be totally fine.
If anyone comes after me, I'll just kill myself.
The English translators turned that into:
I'm a guest character designer for the game, and Naka-san is a good friend of mine.
I usually write comics for the Japanese market, and one of them has him as the main character.
There is only one thing I hate in this world - deadlines!
They kind of wimped out, but I don't really blame them.