Can somebody help!!
try comparing your ajax payload between http mode and https mode.
You are bound to see some difference in how the jsessionid session cookie is being handled in each case.
You can use Http Live Headers plugin of FireFox or wireshark as a tool for this.
I am wondering if your main page is in https mode, but the ajax requests are being made in http mode? However, this does not seem likely from your code pasting since looks like you are using relative links.
Anyways, see what you find out by inspecting the ajax traffic in each mode