IPod Touch 3G replacement battery not living up to what was promised

Question

I have had my iPod touch for almost 4 years. The battery started to run down (loose charge more quickly or just not charge up all the way) about 3 to 6 months ago. I took it in to the Apple shop and they gave me a replacement iPod touch 3G after I paid the battery replacement fee. This gave me a 90 warranty on the fix.
I took the new iPod touch home and charged it up and set it up as a new iPod Touch. No restore. After doing this, I used it for about 30 minutes reading a book. Then it gave me a "20% battery remaining" message. After 30 minutes. So I killed the book software and loaded the battery monitoring software. It showed that, sure enough, I only had 20% battery remaining. But, as I watched, it jumped up to 25%. And then up again to 35%. So I went to plug it into the computer to charge. When I did, it jumped up to 80% charged as soon as I plugged it in. I unlocked it and, on the batter monitoring app, it stated I had an 85% charge. So I charged it back to full then unplugged it again. This time I restarted it, hoping this was just some boot error. It did the same thing repeatedly over the next few days. It would give me a "battery 20% charge" warning, then jumping up to between 35% and 70% as I watched. Then back down to 20% again like some drunk metronome.
I took it back to the apple store and told them my problem. Realizing that this is an old iPod Touch model and future replacements would be similar if not worse, I offered to pay the rest of the money needed to just purchase an iPod Touch 4G. As in, take the original amount paid for the repair, as I had not gotten a battery replacement that worked, and add to that to make up the difference to purchase the newer one with a good, working battery.
This was refused. Instead I was given another iPod Touch 3G to take home. And, again, this one is doing the same thing as the first replacement I received. If I had not been there to see that there were, in fact, two different iPod Touches involved, I would have thought that it was the same one. This newest one has the same drunk metronome battery as the last "new" one.
I have been an Apple customer for many years now and the offer is still open to just pay the rest of the difference to upgrade to an iPod Touch 4. Because I don't want to and cannot play iPod Touch roulette via mail returns for the next month until I finally get one that has a working battery. That and the fact that it costs money for me to get to the nearest Apple store every time I go. So going any more would eat up any money saved on getting that original battery replacement back. But Apple would keep that money and it wouldn't have done what they said they would do. Which is, replace the battery with a working one.

Answer 1

It would have been difficult to take up the problem with the manager of the Apple store as I live in Japan and the manager is Japanese and doesn't speak English.
I did go through many discharge cycles, yes.
That may true and the percentage indicators used in battery information apps may not be reporting the correct percentage. However, when the iPod Touch itself is giving me the 20% battery life remaining warning and then going back up to almost 50% then back down to 20% and displaying a warning 4 times in 10 minutes for two separate iPod Touches, I don't think it is the percentage indicator's that could be wrong on two consecutive iPod Touches. Especially given that the original iPod touch I had, even with the failing battery it had inside of it, did not bounce around that much... Or at all.