Normally when I reach my question limit it tells me a date when I can ask again. Now it just says:
Sorry, we are no longer accepting questions from this account. See the Help Center to learn more.
When will this be lifted?
How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account?
Automatic bans never expire or "time out." This means that you cannot simply wait for a certain amount of time. If you do not take action, you will never be allowed to post again. The only way for the ban to be lifted is by contributing positively to the site in other ways.
Moderators cannot lift the ban.
Before you do anything else, fix your existing posts! As noted above, down-votes cast by the rest of the community factor into the ban - so the single best thing you can do to get it lifted is to address any objections raised by others. Were your past questions unclear? Did they fail to show any effort on your part? Poorly worded, titled, formatted, and overly long or short? Then fix them!
Note the emphasis on fixing. Do not delete your posts. As explained above, deleted questions (if less than 30 days old when deleted) do still count towards the question ban. Deleting your posts does not help to lift the ban. Only fixing does! Under some conditions you can see a list of your own deleted questions and answers.
If you are banned from asking questions, then writing a few quality answers that get upvoted might enable you to ask questions again. But as the internals of the filter are secret, there is no way to know for sure.
If you really, really think the ban is an error, then email the team directly using the "contact us" link provided at the bottom of every page. But note that reactivation of banned accounts is not a high priority.