My account can't ask questions in Stack Overflow because I received several downvotes. I've edited my posts several times and answered several questions, but I still can't ask a question.
How many downvotes can an account get?
closed as too localized by Toon Krijthe, kiamlaluno, yhw42, Time Traveling Bobby, John Saunders Sep 10 '12 at 1:06
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We don't reveal the exact criteria for this block for obvious reasons - knowing what will trigger it would make it far too easy to game, defeating the purpose. Any asker's goal shouldn't be to dodge the bullet by getting just under the limit of downvotes, but to post questions that are upvoted instead.
You can read more about the motivation behind this block as well as some tips on what to do if you hit it here.
Since you already hit the block, you have to get the community to trust you again by convincing them that your existing questions are worth upvoting. Right now, they're still mostly downvoted or not voted on at all.
I suggest following the tips in the meta post I linked above and the How to Ask page. Use proper English as much as you can, clear sentences, concise code that reproduces your problems. With luck, folks here on meta will be kind enough to review your questions and vote on the ones they deem good.
Since Anna already took care of the implied question, I'll answer the literal question.
There is no limit to the number of downvotes an account can get. Or, more accurately, there is no limit to the number of times a given user's posts can be downvoted, since there is no such thing as voting directly on accounts.
No matter how many downvotes you receive, your reputation can never fall below 1. However, getting downvoted a lot can have other effects, as you have already discovered with your question ban.