How to maintain one active login session in Flex application?
Try storing login info in local SharedObject(). or in cookie using cookie if you are using any server side language. Have a look at this. 2 last answers.
is it possible to value store cookies in Flash or Flex? - Stack Overflow
Cookies
How do Cookies work in Flex? | Adobe Community
Shared Object
SharedObject - Adobe ActionScript® 3 (AS3 ) API Reference
Flex® Developers & Development: Local Shared Object (Flash Cookie)
Adobe Flex 4 * Storing persistent data with the SharedObject class
Hope it will help.