You have to ask at least one new question on 100 separate days. The earliest time you can get this badge is therefore after 100 days of participating on the site, where you ask one well-received, not-closed, new question each day.
For example: if you ask one today, it counts as one. If you then ask two more questions tomorrow, they count as one for that day and your total will be two. If you then ask ten questions the day after tomorrow, those will, again, only count as one towards your progress and you will have a total of three after these three separate days.
You can make at most one count progress per day. Basically, the goal of the badge is to encourage continuous participation over a long time instead of spamming a hundred somewhat acceptable questions on the site to hunt this badge.
To be well-received, the question must have a net positive vote count. That means a question with +3/-5 and therefore a total of -2 doesn't count. A question with +0/-0 doesn't count. It needs to be something like +3/-2 resulting in a net +1 or something higher.
You also need to show that you are not simply spamming the site every day in hopes of getting a positive question every now and then. That means that if half of your questions are closed and/or deleted, you don't have a "positive question record".
The script that checks your progress runs once daily at the end of the UTC day.
A question also only counts if it hasn't been closed at any point on the first day. Even if it gets reopened before the script runs, a one-time-closure makes it a question that belongs to the "closed" category. As @Laurel points out in Why doesn't my curious badge count all my well received questions? (emphasis mine):
If you ask at least one well-received question in a UTC day and none of your questions that day are deleted, downvoted, or closed, you get one more day of credit toward the badge.
As a real example I looked at the OP's profile:
If you only ask one question, you can only get one count towards that badge. You need to ask a new question on 100 separate days. According to your profile, your progress is currently at 61/100. That means the earliest date you can possibly get this badge is in 39 days. And that is only if you ask one new well-received (and therefore positively voted), not-closed question each day from today on. Your total question count right now is 76, which means that you might have asked multiple questions on some days before or had some of them closed/downvoted. You therefore need at least 115 questions total to be eligible for the badge.
The basic problem is that the sentence
Ask a well-received question on 100 separate days, and maintain a positive question record.
basically means something like
- Ask a new question each day. If, at the end of the day, it has a positive total vote count and was never closed throughout that day it counts as one well-received question.
- If you do this for a total of 100 days, meaning you have asked a total of at least 100 well-received questions, you can get this badge.
- But if more than half of your total questions are negatively voted or closed/deleted, you are not eligible for this badge.
It's important to note that the above says "closed" in a few instances. A question is disqualified when the question is put on hold as every question is first put on hold and only "closed" after 7 days, which wouldn't make sense in combination with this badge which only looks at the first day. You can see that in the linked discussion about the "Curious" badge, which is basically the bronze version of Socratic, and this question, which was put on hold and didn't count for the person that asked the linked question.
A question that is put on hold, even briefly, is disqualified for that day. And it also disqualifies any other questions you might post that day.