imap-not-running weirdness with Gnus 5.10.7

[Emin Martinian]

I'm a happy Gnus user but recently I've been having problems and
getting the message imap-not-running with Gnus 5.10.7.  It looks like
the imap connection dies if I haven't done anything for a while.  This
doesn't seem like a problem because it often gets restarted when I
check for new mail.

The disturbing thing is that sometimes I try to send an email and get
the imap-not-running message and the buffer containing the email does
not go away.  At this point, I don't know if the mail
has been sent or not.  I have a Gcc:m/out/sent-mail-2005 field
specified for all my mails, so that I could use that to check if an
email has been sent, but when I get the imap-not-running
message this field seems to be ignored.  Specifically, people have
complained about me sending them multiple copies of emails when I only
have one copy in my Gcc box.

Thanks in advance for any help,
-Emin Martinian