Would it be reasonably for me to suggest having the discussion sooner
so that any issues can be corrected?
Yes, it would be reasonable. And no, you're not being paranoid.
But I would make this request over email if I were you. First, send the email, then make the request in person. This memorializes your request. If you don't have your boss's email address, you should send a text.
Your request needs to be two-pronged. First, it needs to address this unexcused no-show no-call absence (which is very serious). And second, your request needs to uncover any of the other concerns she may have hinted at. Because if you don't know what those other concerns are, there is really no way for you to take any kind of corrective action in the meantime otherwise.
Which begs the question, why wait a couple of weeks before correcting your behavior? This makes no sense unless her plan is to fire you.
I told her that I wasn't informed I had one and had checked my call
history for the day prior to the shift.
Call history can be altered. You just need to long-press on a logged phone number for it to disappear.
If your cell phone provider can provide of a log of incoming phone calls, I'd suggest you order a paper copy from them.
She said she thought she had
called me on another day, other than the one the day prior. Should I
follow up further?
Clearly, you should.
If you don't, they may make their decision of not keeping you at the very last minute when you're at 249 hours, and then, they may not have time to talk to you to get your side of the story.
Also, if the industry of your employer is tied to the Christmas shopping season, keep in mind that you have the most leverage right now, just before Christmas. If you wait when they're less busy to talk to them, that's the time they may be looking to trim their workforce (especially their workforce which is still on probation and which doesn't have union representation yet).
Furthermore, every day this discussion gets delayed. Everyone's memory will get fuzzier and fuzzier.
And last but not least, if your reputation is tarnished now, and word spreads around your employer, the more time you wait, the more difficult it will be to get those allegations recanted by your manager and get your reputation repaired. Because by then, it will be the reputation of your manager which will be on the line.