Note that I have not used Rufus before and am not a Kali expert. However I have used very similar tools.
It sounds like persistence is not working and to get it working you will need to reinstall. I can see persistence is mentioned in two different ways:
It's not immediately clear if these are expected to work together or if Kali's persistence is compatible with Rufus at all. The problem is that Rufus isn't just an imaging tool. It's unboxing the ISO image and building a system on a USB for you. Usually this involves packaging files into a read-only "casper" file. Typically Rufus Persistence would up a second partition partition and overlay this over the read-only file.
Kali's ISO is already an image of a bootable live-linux; it doesn't need to be unboxed and assembled by Rufus. Kali themselves recommend just flashing it to your USB with Etcher. I suspect the persistence option offered by Kali either need's Rufus persistence to be enabled or is completely incompatible with Rufus. I can't easily tell you which.
Your simplest option may be just to loop back around and use Etcher instead of Rufus.
Alternatively you might want to just install directly onto your SSD. Boot from your USB flash drive, plug in your SSD and select "Install" on Kali's boot menu. Warning: There's a risk when doing this that the installer will corrupt your main OS (Windows?). If at all possible you should unplug your main hard drive before proceeding to ensure Kali's installer cannot access it and corrupt it.