Happening to me on Manjaro/Plasma 6.0.5 (Wayland)
Having the same problem on Arch Linux with Plasma 6.0.5 (X11) and systemd. Using sudo chown -R -v $USER:$USER /home/$USER seems to make any previous changes persist, but you must run this every time you pin or reorder task manager items.
After some further experimentation I have found a temporary fix. Not sure if these prior steps affected the outcome but I deleted “plasma-org.kde.plasma” file from .config and logged back in and then deleted the panel and recreated it. What seems to be actually working is making changes to the panel, logging out, then logging back in, and then changes will persist after a reboot.
Same problem. Something that I found out is that if I make changes to panel and then alternate between themes the changes persist.
I have the same issue and none of those steps fixed the issue for me.
I’m running the lastest kde plasma on x11 Archlinux
Signed up to let you know I have the same issue on Arch/KDE, also with systemd.
At this point we’ve actually fixed it. 
See 481113 – When not using Systemd or Plasma's Systemd session launch integration, changes to pinned apps are not saved when Plasmashell quits. The fix is in Plasma 6.1, which will be released in 3 days.
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This was posted back in March? Still apps won’t stay pinned to the taskbar, and then I get a bunch of default apps re-pinned that I removed. How is this even possible in a major release upgrade? Is that not one of the first things you would notice with even the laziest of QA?
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None of the developers noticed it because it only happens with certain non-default settings.
None of the users affected were able to help us figure out what settings cause it for a long time.
It’s fixed for realsies in Plasma 6.1.