The low voltage point that you recharge a lithium ion cell (the rechargeables we use) is one of the factors that determine its service life: the number of recharges you get from a battery. In theory an IMR cell will do 500 recharges but this is not going to happen in reality, 200 would be a good life in the real world. The main things that affect it are the duty cycle and the recharge cycle (forgetting about things like ambient temperature etc. here), so:
1. The low voltage point that you never go below when taking the cell out and recharging it.
2. The high voltage point that you never go above when recharging it.
3. The maximum amp discharge rate you subject it to, in service.
4. The maximum milliamp charge rate you subject it to, when recharging.
So if you recharge the battery when it drops to (say) 3.5 volts at the lowest, never recharge it above 3.17 volts (we know this point as it has been well-researched), never ask it to deliver more than a few amps, and always trickle charge it at a very low rate (certainly less then 500 mA and most likely at 250 mA even for a 2000mAh cell), then you would expect to get somewhere near the maximum service life (number of recharges).
No one is going to do that (AFAIK) as it's a pain compared to just shelling out $10 for a new batt. We recharge them to 4.2 volts (too much), drop them to 3.2 volts (too low), ask them to deliver 20 amps (too high), and recharge them at 1 amp (1000 mAh - too fast). They work fine but you get around half the service life, maybe less. The same thing applies to humans, a full service life sounds like a good idea but who wants to live in a monastery and live on bread and carrots. It's a trade-off.