Well I'm not a qualified electrician or anything like that, but I have dabbled with electronics a bit in the past and HO/OO gauge railways as well so I'm used to playing with circuitry.
It doesn't surprise me that the AAA is dying before the 9v Lithium to be honest. For a start the 9v Lithium would be likely to outlast any AAA even if the AAA were a Lithium as the 9v's capacity is going to be much higher (the mah/hour rating). However I suspect your problem is more likely to be that there is a resistance differential between the two cells and the AAA is simply being drained before the 9v Lithium. As I'm sure you've seen with many instruction manuals it always advises against using different brands or different charge levels of batteries, it is specifically for this reason because battery characteristics change as they are drained I believe.
I'll do a bit of research and see what I can find, it may be possible that you can run the two together using a component or two.
As for the sound no longer working, that's probably because it has a sound/processor chip which is designed to work at a specific voltage, so you'd probably need to put a voltage regulator between the batteries and circuitry - assuming its not blown already lol!
It doesn't surprise me that the AAA is dying before the 9v Lithium to be honest. For a start the 9v Lithium would be likely to outlast any AAA even if the AAA were a Lithium as the 9v's capacity is going to be much higher (the mah/hour rating). However I suspect your problem is more likely to be that there is a resistance differential between the two cells and the AAA is simply being drained before the 9v Lithium. As I'm sure you've seen with many instruction manuals it always advises against using different brands or different charge levels of batteries, it is specifically for this reason because battery characteristics change as they are drained I believe.
I'll do a bit of research and see what I can find, it may be possible that you can run the two together using a component or two.
As for the sound no longer working, that's probably because it has a sound/processor chip which is designed to work at a specific voltage, so you'd probably need to put a voltage regulator between the batteries and circuitry - assuming its not blown already lol!