Number of inquiries in past (12 months, iirc) does have a negative effect on your credit score.
I believe you can expect a 5-15 pt drop for an inquiry?
I'm sure there is a 'maximum' number of pts you can lose.
Number of open accts also has a factor. If you are churning, you're not increasing the number of open accts...and that is good.

If you are not planning to buy a house / car / refinance loan / etc, letting your credit score fluctuate doesn't have a terrible effect. Stop churning, wait for the inquiries to clear, and your score will go up again.
If you have good credit, churning probably wont' drop you below 'pretty good' credit.