To start with, Bluetooth eats power fast. Phones for example, that have Bluetooth enabled, drain much faster than the same phone with it turned off. Be sure to turn OFF the power switch on your mouse when it's not in use and that will at least help to conserve your battery life. Second, don't buy cheap batteries, or buy rechargeable ones. If it's a very low cost wireless mouse it may simply be defective or have a very short signal range.
I'd try premium batteries first and shut the switch off when it's not in use. If that fails to help, I'd replace or return the unit.