They are right, it can be 2 weeks before you go into labor, but since you are this close to the end, I bet in the next 2 days you will go into labor. I hope!
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Losing your plug in all honesty, has nothing to do with when labor will begin. Your plug can even regenerate over time. I lost mine all at one and it never regenerated itself as far as I could tell, but I lost it 3 weeks before I ever went into labor.
Re: mucas plug
I also started losing mine in pieces the last few days (had them swept on monday) but i am still hoping she comes soon!
No one can tell you when you'll go into labor--you can lose your mucus plug over several weeks.
With that said, with DD1, I had my membranes stripped at my 39 week appt and lost my mucus plug and went into labor less than 48 hours later.