We have the same issue, with all our users.
The email account is greyed out after upgrade to iOS 11(.0.2)
Everything was working fine before the upgrade.
iOS 11 is doing something different.
A quick note of my findings...
As we don't use an official certificate, I added our CA as trusted CA on my iPhone, but that did not solve anything.
Than I toke a look at the server-side. Our situation is like this (a bit more technical here, and not easy to explain in a language that is not mine, but it might be relevant):
The imap-server I connect to, "imap.company.com" is a cyrus imap server.
In fact, it is a frontend for 2 imap backends ("imap-user.company.com" which stores the regular user mailboxes and "imap-shared.company.com" on which we store shared mailboxes).
If I configure the mailaccount on my iPhone with iOS11 to use as incoming mailserver directly the backend "imap-user.company.com", I do not have the "greyed-out" issue (but I cannot read the mail in the shared mailboxes).
Neither do I have an issue when I connect it to the other backend imapserver "imap-shared.company.com".
But connecting to the frontent "imap.company.com" makes the account become greyed out in iOS 11.
For the connections from a iPhone with iOS 11, I see these messages appearing in the logging on the "imap.company.com" imap-server:
...
Oct 11 10:29:40 imap cyrus/imaps[25800]: IOERROR: opening index user.username: System I/O error
Oct 11 10:29:40 imap cyrus/imaps[25800]: IOERROR: opening index user.username.Trash: Archive I/O error
Oct 11 10:29:40 imap cyrus/imaps[25800]: IOERROR: opening index user.username.Trash: Deleted Messages I/O error
Oct 11 10:29:40 imap cyrus/imaps[25800]: IOERROR: opening index user.username.Trash: Sent Messages I/O error
...
What is the Mail app trying to do here that it did not try in previous versions?