Stefan,
I'm not sure what's happening there. When you enable/disable caching, can you tell me what specific setting or extension you're using? Is this the default Joomla -> Global Configuration caching setting, or do you have a 3rd party extension? If it's the Joomla setting, are you using Conservative or Progressive? Do you have Memcache, APC or any other PHP caching enabled?
Also, in the Advanced parameters area of the SCLogin module, there is a way to disable caching for the module. I'd try that as well to see if that improves things.
Anything you let us know about your config will help us narrow things down. There are many sites that use the SCLogin module with caching and have no issues. We'll need to see what's causing the issue on your site.
Thanks,
Alex