iCloud IMAP not working from El Capitan Mail

I'm trying to access my iCloud email over IMAP using OS X Mail in El Capitan. I'm following the instructions here:

iCloud: Mail server settings for email clients - Apple Support

Note that I do not want to set this up as a normal iCloud email account, but instead as generic IMAP. (Because I need to use an alias other than my @icloud.com address, and the normal iCloud account option does not support these aliases.)

However, the connection has been unreliable, sometimes working but frequently giving me "Service temporarily unavailable" errors for hours at a time. Tonight, I can't get it to work at all. I deleted and recreated the account, and tried different variations on my user name, but it will not allow me to connect.

Here are the relevant log lines from Connection Doctor:

INITIATING CONNECTION Oct 23 21:57:09.282 host:imap.mail.me.com -- port:993 -- socket:0x0 -- thread:0x7f9f1cc8c8e0

CONNECTED Oct 23 21:57:09.594 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

READ Oct 23 21:57:09.654 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

* OK [CAPABILITY mr11p00im-iscream009 15E43 XAPPLEPUSHSERVICE IMAP4 IMAP4rev1 SASL-IR AUTH=ATOKEN AUTH=PLAIN] iSCREAM ready to rumble (15E43-20056:11915) mr11p00im-iscream009 [16:707:03:57:09:8B]

WROTE Oct 23 21:57:09.656 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

3.372 AUTHENTICATE PLAIN (*** 44 bytes hidden ***)

READ Oct 23 21:57:09.740 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

3.372 NO [UNAVAILABLE] Service temporarily unavailable

WROTE Oct 23 21:57:09.741 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

4.372 AUTHENTICATE PLAIN (*** 32 bytes hidden ***)

READ Oct 23 21:57:09.805 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

4.372 NO [AUTHENTICATIONFAILED] Authentication failed

WROTE Oct 23 21:57:09.806 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

5.372 LOGIN [my username here] **********

READ Oct 23 21:57:09.894 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

5.372 NO [UNAVAILABLE] Service temporarily unavailable

WROTE Oct 23 21:57:09.895 [kCFStreamSocketSecurityLevelTLSv1_0] -- host:imap.mail.me.com -- port:993 -- socket:0x7f9f1a4f5030 -- thread:0x7f9f1cc8c8e0

6.372 LOGOUT