I remember being taught that there would be another testing period at the end of the 1000 years. Those that passed that final test would receive the gift of 'everlasting life'. Not immortality. Immortality was granted only to those called to heaven. (Even the angels were not granted immortality, as I recall.)
I think it was explained to me that perfection did not mean 'would not sin'. Rather it was ability to make perfect, knowing decisions. Not necessarily in line with Jehovah's purposes. Free-will would still exist.
Then again, I could have foggy memmory (too much fear, obligation, and guilt to think clearly...!)
-Aude.