encrypted disk tmage problems on Intel iMac

Model # MB952LL/A running Mac OS X 10.6.5 (10H574)
When using encrypted disk images after ejecting it's possible to reopen the image without re-entering the password. After some time or something else, I'm not sure what, you then have to use the password. I'm not sure if this is a problem or normal. Any information would be appreciated.
Thanks

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