Eneloop rechargable batteries for mouse?
Different types of batteries have different discharge rates when not in use due to a number of factors including type of battery, state of charge, charging current, ambient temperature and other factors (See here for more on self discharge). 

I previously confused ESR with self discharge, where ESR determines the maximum current the battery can provide. For more information on the characteristics of rechargeable batteries.

According to the Wikipedia page on Eneloop batteries, they have a low discharge rate, making them better for items that are used infrequently. 

Also below is a chart that was provided to me by a professor previously that shows some of the advantages/disadvantages of different types of batteries: