I was experiencing exactly what you described but it only started after I installed the secure_pages module. I used firebug for firefox to figure out that the ajax request for the CC info div wasn't responding 1/2 the time. I went into secure pages and added "cart/checkout/payment_details/*" to the ignore pages since that was the URL that was being flaky. Now it works fine. However I don't know for sure if that opened up any security holes

Hope that helps.