Hello,
I have had this problem intermittently although I could confirm the application server domain was running (PSADMIN - Server Status) and could be signed into using the Windows PeopleTools client. The crazy thing about it was that the development servers worked without any problems, but the production servers would experience the problem
The final resolution I can to through a conversation with with a PeopleSoft Customer Connection consultant. He stated that if the server has more than one network interface card (more than one IP address), you should use the static IP address in the PeopleSoft configurations (application server domains, process scheduler server agent, WebLogic, etc.). Don't use the machine (hostname).
Looking back at the development servers, those server have one NIC active, but the production server have two more more NICs active.
Once I replaced the hostname with the IP address, the "application server domain down" messages went away.
I have always perferred to use the PSMACH value and let PeopleSoft resolve it. I have not been able to confirm if this problem will exist with the use of the PSMACH variable, but using the IP address has worked so far.