Others with this issue have contacted support to allow remote access with the problem still persisting. This post is now just over 2 years old, so this is way more likely a win11 bug that needs to be fixed by Microsoft developers rather than something to contact support for.
I have been dealing with this issue since I "upgraded" (although in many ways it was a downgrade) from win10 to win11 about 4 months ago. Many people warned me to not upgrade because despite being years old, win11 was buggy and removed many customizations; but being in the tech industry, I figured being up to date was the better option (it was not). There are so many small bugs that add up to me wanting to "downgrade" back to win10. There used to be more customizations that made my work flow much easier, but now I'm left frustrated.
Like many others commenting on this post, I've tried so many workarounds to keep the taskbar hidden as well as tried to customize taskbar in ways that are no longer customizable (for example, changing the size of the taskbar. You would think this customization is an obvious one to keep from win10, not just for aesthetic and workflow reasons but for accessibility reasons as well. Another example, the option to have mini icons on the taskbar, for when you resize the taskbar to a smaller size and have more real-estate on your screen - I really miss these options).
As for the taskbar continuously unhiding, my issues are much like the others here. Since I have started using win11, the 'automatically hide the taskbar' option has remained checked even when the taskbar unhides itself, and unchecking and checking again does not work. Restarting my PC after various changes does not work. Like others here, it seems to unhide permanently every time I get a notification from any app on my PC, as well as after it has gone to sleep, and also when I turn it on. I have dual monitors, but people on this post with only 1 monitor have been having the same issues.
How I've been managing this, like others here, is I have been restarting windows explorer in the task manager, and that hides the taskbar... but only until it unhides itself again, which is incredibly frequent. I have tried turning off notifications to see if it helps, but the problem persists at about the same frequency.
I should not have to resort to sacrificing other things to make this work when it is supposed to work correctly. It is incredibly annoying to have to restart windows explorer every time it happens, and I am not alone in this - other commenters here (at least 3 I read) even spent time to script their own app to do it for them when the taskbar unhides permanently!
It is ridiculous that this issue is not fixed yet. If windows was open source, the issue would have been fixed almost immediately, along with many customizations and other accessibility and privacy options - but big companies like Microsoft love their secrets and hoarding users' data, so this would never happen. But one can dream.
I largely hope the activity on this post will lead to changes in win11, but more than likely this issue will continue to be disregarded.
Please prove me wrong, Microsoft - please fix this, and please bring back the customizations to the taskbar.