Is losing posting privileges due to many downvotes / closed questions, a permanent thing?
So, that's it?
To add to stoicfury's post, you should read What can I do when getting "We are no longer accepting questions/answers from this account"?
There are different types of privileges here. Privileges that are associated to certain reputation thresholds are gained or lost at those thresholds. So those can come and go.
But the more fundamental privileges of asking or answering questions can also be taken away. They can be taken away temporarily through suspensions (which are done manually by moderators). Or there are automatic bans that are done by the system when a user posts many extremely bad posts.
These are not necessarily permanent, but they are not necessarily temporary either. This is what the meta post I linked to above is all about. But one thing to really take to heart is the only way for a ban to be lifted is to contribute positively in other ways.
One can lose posting privileges in two ways: through being banned or suspended. Bans are typically permanent (but they don't technically have to be), suspensions are temporary.