SSL problem after process to checkout in view cart page

My unsecure base url: http://www.mydomain.com
My secure base url: https://mydomain.com (without www)

We're not forces for all pages. We only for Checkout / login / Wishlist / etc...

My Problem is:
After add to cart for my product, it going to view cart page and then try to process to checkout but can't checkout, only reload and stay in view cart page. So i try to check in view-source code at Process to Checkout button, it is showing secure url https://mydomain.com/onepage. I don't know why page not going to checkout page.

If i using chrome browser, after two (or) three time to click checkout button, it is process to checkout with ssl.
if i using IE (or) mozilla, it not process to checkout page. Sometime, after two (or) three time to click checkout button, shopping cart is empty.. and so try to re-add product again and re-checkout again.. but still can't now.

Back-end Setting:
Add Store Code to URL: No
Auto-redirect to Base URL: Yes (302 Found)
Use Web Server Rewrites: Yes
Use Secure URLs in Frontend: Yes
Use Secure URLs in Admin: No
Use SID on Frontend: No