Playback glitches unless connected to power

Overview:

My SSD upgraded iPod will fail to play songs and skip multiple at once - the songs it does play will only play for a couple of minutes before a brief silence followed by the song skipping before the end. However, the iPod works fine when connected to power - i.e. in the car via USB connection or wall plug.

History:

I chose to replace the HDD after it corrupted and was not recognised by my PC. Previously no playback issues were experienced (until the HDD corrupted). The replacement SSD can be found here. A larger capacity replacement battery was also fitted.

Edit: Could be worth noting that original capacity was 80GB, with replacement SSD increasing to 128GB.

Thoughts:

At first I thought this could be a battery issue, however upon changing back to the original battery the issue still persisted, except for when connected to power (same situation as the replacement battery). The iPod doesn't actually show its connected to power when plugged in, however as soon as the cable is removed, the play back issues return. Also, I am confident the files on the iPod itself are fine/not corrupted, as they all play without issue when connected to power.

Anyone have any ideas where the problem could be?

Thanks for your help!