After you know what the liveness probe is doing, you can edit the workload to remove it, then access the container in the pod to dig further into the issue.
A couple of possibilities are:
1. If the workload is fine and only failing due to the livenessProbe, make a better livenessProbe because the check is probably wrong.
2. Else troubleshoot mostly like you normally would and fix whatever is causing postgresql to not work right.