Interesting that you posted that question at this time. As fate would have it I'm having the same exact issue and was in fact getting ready to post to ask for some help with the same issue. Got my Classic IV out for a bit of practice yesterday and noticed the E string side stud was up a bit. I had the bridge set about level (I've read plenty of times that the rear of the bridge should be lower than the front side), so I thought I'd readjust it so the rear was lower than the front. That just made things way worse, now both are pulling out and won't stay in despite pushing them back down and readjusting the bridge a couple of times. First time I've encountered this, the Bird is a 2008 model and I've owned it a couple of years now.
Now, I've read plenty before on how others have addressed the fix for this and I THINK I have a fair idea of how to go about it, but rather than sort through several hundred pages of this thread thought I'd just ask again knowing that several of you here have the ready information to share. So thank you in advance for helping myself and @rodv66 get our Birds straightened out, all help sincerely appreciated.