In general, you don’t lose privileges by asking lots of questions, you lose them by asking low-quality questions. And unless you’re very abusive (e.g. spamming links to your questions, trivial edits to bump for views), the worse you can get is a temporary ban on asking questions.
Initially, you might get your ability to ask questions be rate-limited:
We realize that when you come to ask questions, you're in a bit of a hurry, because you're looking for an answer to help you get your work done. This has resulted in a history of questions that have been poorly-received by our community – so we're asking you to slow down until you've learned to ask better questions.
(Some of the wording is a little inappropriate for this site, as this is mostly recreational rather than for work: this text is copied verbatim from Stack Overflow.)
If you continue to ask poor quality questions, then you might get a question ban:
Stack Exchange has automatic filters in place to ban questions from accounts that have contributed many low-quality questions in the past. These filters help keep the quality of our sites high. The exact formula for the bans is not disclosed, but users are only banned if they have a significant number of heavily down-voted, zero-voted, or deleted posts. One or two bad posts will not cause you to be blocked from using the site.
Both of those are automatically triggered by the system.
I believe diamond moderators can also issue temporary bans for abusive behaviour, but common sense is usually enough to avoid that sort of ban. If you’re getting close to a manual ban for too many questions, they may also reach out to you privately first.
There are various pages in the help section about how to ask good, high-quality questions:
I note from your main profile that you don’t have any questions with a negative score or which have been closed (yet). You won’t be able to keep asking questions at 3 per day forever: we have a 50 question per month limit, but personally I don’t think you need to worry about a question ban if you continue at the current rate.