Every time I start gameplay or enter a door, this webpage opens: http://www.macromedia.com/support/documentation/en/flashplayer/help/settings_manager03.html
Flash has limited storage space. You have to click the flash player object on the page to open the storage settings and increase the amount of data Flash is allowed to save. I cannot do this for you, this is the price of playing Red Rogue in a browser.
I recommend downloading the desktop version instead.