is apple mail server having troubles

Problems with iPhones, Wi-Fi networks with bad routers or transient interference, ISP network issues, regional IP routing or bogus BGP info, and occasionally even problems Apple’s servers can and do happen, yes.

Per Apple system status, seems some folks working for Apple server support are having a Bad Day:

paulfromcolorado wrote:

Yeah, I saw this on my desktop iMac on Monday morning, April 26 also. And I'm seeing it again right now (Tuesday, May 4, 5:08 PM MDT), although this time it seems to be even more messed up. So how do I get to that System Status dialog box for the Mail server?

Problems with Macs, Wi-Fi networks with bad or marginal routers or transient interference, bad Ethernet cables, ISP network issues, regional IP routing or bogus BGP info, and occasionally even problems Apple’s servers can and do happen.

Per Apple system status, seems the servers are running correctly today, though the outage may have been transient.

Blue-text here in ASC is a link to more information, too.

But should there be issues with your iMac, you’ll also need to check your iMac setup, your local network, and the other pieces of what is a complex configuration of hardware and software and firmware between you and your mail, until you can determine what is wrong for your case. Apple Server status is easy to check, yes. But when troubleshooting computer and networking problems, it’s also best to avoid assuming culprit.

Yeah, I saw this on my desktop iMac on Monday morning, April 26 also. And I'm seeing it again right now (Tuesday, May 4, 5:08 PM MDT), although this time it seems to be even more messed up. So how do I get to that System Status dialog box for the Mail server?

The link is posted in the Apple Recommended answer. - Apple - Support - System Status

Why? Are you having issues?

Same. Since Friday. Any explanation?