Audio books on iPod touch
I bought two audio books through iTunes. I can listen to them at home. But when I tried to listen to them at the gym, they wouldn't play.
iPod, iOS 15
If you mean that you can play them at home on your iPod, but not in the gym (on your iPod), that suggests that the audiobooks are not downloaded to your iPod and that when played at home, they are being streamed via your home's Wi-Fi.
Download them to your iPod and then you will be able to play them away from home.