Mail stopped connecting to imap servers

This morning my MacMini running 10.9.5 was not responsive and the fan was running. I rebooted. It came back apparently ok but Mail could no longer connect to imap.google.com or smtp.google.com. The connection doctor only says:

INITIATING CONNECTION May 23 14:58:26.011 host:smtp.gmail.com -- port:587 -- socket:0x0 -- thread:0x60000127f780

INITIATING CONNECTION May 23 14:58:26.012 host:imap.gmail.com -- port:993 -- socket:0x0 -- thread:0x608001c67cc0

In the log I find:

5/23/15 2:58:26.377 PM Mail[754]: [LogSocketErrors] Connecting failed for socket: 0x6000004da4e0, error: Error Domain=NSPOSIXErrorDomain Code=65 "The operation couldn’t be completed. No route to host"

I can connect to the host:

telnet smtp.gmail.com 993

Trying 74.125.28.108...

Connected to gmail-smtp-msa.l.google.com.

Escape character is '^]'.

I have not done any upgrades recently. I repaired permissions. Rebooted more than once. Checked the filesystem. Removed and reinstalled my mail account.

My Macbook, sitting next to my mini (on the same net hub) has no problem with Mail.