Multiple Windows Authentication Prompts after F5 Authentication

The AD delegation account (host/kerberos_user) must have the SPN of each and every account that it is allowed to delegate to. You've indicated that the pool members' individual SPNs are assigned, but if you're attempting to request a ticket for http/ssrs.example.com, then that SPN also needs to be in the delegation list. But more important, if Kerberos SSO works when specifying the server SPN (server1.example.com), that's a good indication that the ssrs account is indeed not the owner of the service.