Question / Problem:
My partner level user doesn't get approval alerts even if we have set the alert setting to daily for the customer workflow.
Answer / Solution:
The explanation is that even if the workflow is on the customer level, you have to setup the alerts on partner level if the user is on partner level. Since your user is on partner level, you have to setup an alert there, to be able to get alerts sent to your user.
Please check the workflow notification alert setting on partner level. Make sure it is set to send alerts.