Disk DMA might help here. It doesn't help much when playing MP3 files, but there's a lot more disk access when playing FLAC. It was disabled due to instabilities. I think those instabilities were due to a CPU cache bug, and I have a workaround. First apply
this patch. Then edit firmware/export/config/ipodvideo.h and uncomment or add "#define HAVE_ATA_DMA". Finally, recompile.
I think your battery might be worn out. When I was playing FLAC, the battery life wasn't too bad, even without DMA. Note that some cheap batteries overstate their capacity.
When the battery is very cold, you're only able to make use of a small fraction of its capacity. When going outside in winter, I put my iPod under clothes to avoid this.
If the problem is hardware cutting off power during disk activity instead of an orderly Rockbox shutdown, it may be possible to avoid that by decreasing the hardware shutoff threshold while the disk is active. I thought about creating a patch, but I'm not sure if it's a good idea. This problem normally means the battery is worn out and/or too cold.