I just charged my 10+ year old (produced 2006) Eneloop with my Lii-500.
The internal resistance of the cell was measured 250mOhm on YR1035, but it showed 45mOhm on Lii-500. The internal resistance measured on my current charger Lii-600 gave me numbers that are similar to that from YR1035.
The cell was stored fully charged not long ago and it took about 20 minutes before Lii-500 stopped charging. The displayed voltage did not go over 1.5V and terminated around 1.48V. When I checked the voltage across the charging pads a few minutes before it ended, the measurement did not go over 1.65V.
I recently learned that internal resistance of NiMH cells tend to shoot up exponentially as they age. Thanks to the recent post by thefreeman I came across a very interesting website that shows how NiMH cells age. See http://aacycler.com/ According to the webpage, the way cells age varies alot. It could be possible that your cell has very high internal resistance.
By the way, my Lii-500 is almost ten years old. So, the charging logic may have changed since.