This is an ancient thread, but I wanted to report that my ISS is still using the original Eneloop rechargeable AA batteries (in C spacers) that I installed shortly after this discussion and there have been no issues. The fan runs 24 hours as expected. I did not get around to installing the double-solar ISS cover, though. I thought it was worth pointing out that these batteries have lasted almost 5 years without issue and I have no reason to believe they are near the end of their useful life yet.
Eneloop is a solid brand. You can actually get a starter kit from Costco right now, on instant rebate. It comes with a wall charger and 12 batteries (8 AA and 4 AAA?), I believe. They advertise the ability to charge and recharge for many cycles, so I am not surprised by your experience. I have a Vantage Vue, so I do not need them, but if I ever upgrade to the VP2, I will certainly go that route.
I have some solar yard lights I have had since 2010. About half of them still work. I should check to see what brand they use. Whatever it is, they've taken a beating in the northern California climate, especially the hot summers.