Crossing from http to https will not cause the problem i described, as long as the domain stays the same.
So for example, going from:
will not cause an issue. http vs. https only changes the port that is used to connect to the web site:
http = port 80
https = port 443
it does not change the domain.
When I test your pages I am not able to reproduce the problem. I will need to be able to reproduce the problem to be able to get an idea of the cause. With out being able to reproduce, I really have no way of knowing what the problem may be.