It happen most of the times, and even if it works, it's most likely temporary: even when I am able to change the description, it usually goes back to showing my old one in a day or so.
I cannot say how long it takes to update the descriptions since, for example, my playlist from august has been reverting to the first description I put at the beginning of the month, despite the fact that I have changed it multiple times after setting the first description. However, for the playlist that I made yesterday, the descriptions have been updated immediately. It's very inconsistent.
We've reported this to the right team and it appears that it's expected behavior for the playlist description to not update instantaneously across all platforms.
If the description is reverting back to a previous state, we recommend you wait longer without changing it while it's syncing. You can also try to update the description using the web player for faster results.
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“With freedom, flowers, books, and the moon, who could not be perfectly happy?” ― Oscar Wilde
That kind of fits in with what i've experienced, but it's definitely hit and miss. The thing about revisions to playlist description "sticking" better if you do it on the web player rather than the desktop app comes as a surprise. I'll have to try that to see if it's easier than my current workaround: copy tracks to new playlist with same name; add revised description to new playlist; delete old one.