I had the same problem and I figured out how to fix it! For Samsungs, Apps ‐> ChatGPT -> Battery -> Unrestricted completely fixed the issue for me, it continues

I had the same problem and I figured out how to fix it! For Samsungs, Apps ‐> ChatGPT -> Battery -> Unrestricted completely fixed the issue for me, it continues thinking/outputting in the background now. Should be a similiar setting for other Android distributions. Basically, it wasn't the app's fault, the OS is just halting it in the background to save battery.