Do too many inquiries cause banks to close your existing accounts?

Can the inquiries cause closure? Yes they can. If the issuer pulls your report, sees the two cards you have and then 4 more inquiries, the issuer could make the determination that you are trying to open too many cards in an effort to run up balances that you would later not pay. If they make this determination, they could either lower your limit or close the account altogether as a way of minimizing their risk. Does this happen? Yes. Will it happen? Who knows.

This sounds like a path down the road to bankruptcy. The ones that approved are still fine, but if you think this is a good idea, it's not. Be very reasonable with the cards yo have. If you're not paying them off immediately, you're taking out stupid loans at 20% a year.