I guess you created both sites on the same IP? Traditional SSL requires a dedicated IP address for every SSL website. When you create two websites on the same IP and enable ssl for both sites then you get SSL over SNI which is not supported by all web browsers and apache versions. See wikipedia article about SNI for details.
So if you want to have two ssl sites that work in all browsers, you need two IP addresses and assign the first site to the first IP and the second site to the second IP. Thats always the case for ssl site, so not a limitation of ispconfig.