We can answer this question... the battery that comes with the Neuralyzer is only a sample or demo battery. It should be replaced with with a domestic name brand battery for best performance as indicated in the instructions. For peak repeat performance (lots of flashes in quick succession) we recommend lithium batteries. For longevity we recommend Alkaline batteries. Its unfortunately a trade off, because as far as we are aware nobody currently produces a battery with both characteristics.
The neuralyzer replica uses the same flash set up as a camera. Not wanting to get too technical, but this has a hefty effect on the recharge rate of any battery. Basically the amount of power sent to the capacitor to charge the flash mechanism. The faster the refresh rate the more times the flash can be used in quick succession. An alkaline battery will last longer and supply power for a longer time but the refresh rate is not as good. You will need to wait longer between flashes.
For this reason several manufacturers offer special batteries designed specifically for cameras. We have found these to offer the best performance. We tried to supply the best battery we could obtain to give the best overall performance, but its not a known brand name and is only intended as a sample. All batteries are not created equal and when flashes involved!
This is not a fault, its just a limitation of the space available inside the prop and the limits of electrical engineering.