Why does not a rechargeable battery last forever?
1.Should all the batteries such as the AA type last forever,since they can get recharged all the time?
2.How about the battery in the cellphone,since they can get recharged?
3.How would I am able to make a rechargeable laptop battery extend its life?
No battery is perfect. They all depend upon a chemical reaction and their constituent parts like electrodes. Over time, oxides build up on electrodes, etc and so with time, temperature, and so many discharge cycles, they start to degrade.
Ditto with a cell phone battery.
First, you need to know the battery type. Lithium ion, lead acid, etc.
Then you need to know and observe the limitations each type has. Some need to be discharged almost completely before recharging while that degrades the life of others, etc. Each battery type will have temperature limitations and some guidelines on how to use it to maximize life.
How to Recharge Batteries