Sometimes Really Simple SSL doesn’t work too well with other plugins. Most of the time this is caused by another plugin blocking the mixed content fixer. We know of compatibility issues with the following plugins:
WP Social SEO Booster (hasn’t been updated in three years, so wouldn’t recommend to use it anyway)
USM Premium (USM support appears to have a fix for this, or they may fix it in the next update)
Genesis Toolbar Extras, thanks to Jon Burr for reporting it
SEO WordPress (Currently under investigation)
Deactivating these plugins should resolve your issues with Really Simple SSL.
If you encounter any plugin compatiblity issues, please share this the comments. In most cases, the problem is that the output buffer is used in a way that is not compatible with Really Simple SSL. For example, in the case of USM, the output buffer wasn’t started properly in some cases, which caused the flushing of the output buffer to flush the Really Simple SSL output buffer.