I have this problem with versions 4.2.3 and 4.30RC3,
didn't try any other.
I have searched the mailing lists and saw several messages with the same problem.
However, no messages with the solution...
My openssl version is 0.9.6h.
I have installed imap (imap-2002a.DEV.SNAP-0212051126) and copied the c-client files as stated in your documentation.

1. configured php with following configure:

/configure --with-apxs=/usr/local/apache/bin/apxs --with-config-file-path=/etc --with-mysql --with-mcrypt --with-openssl=/us
r/local/ssl --with-imap-ssl=/usr/local/lib

output:
checking for IMAP support... no
After running make and make install and restarting apache (DSO module) tried to use imap:
Fatal error:  Call to undefined function:  imap_open() in /var/www/htdocs/tickets/imap_create.php on line 11

2. Tried without "with-imap-ssl", but with "--with-imap":

./configure --with-apxs=/usr/local/apache/bin/apxs --with-config-file-path=/etc --with-mysql --with-mcrypt --with-openssl=/u
sr/local/ssl --with-imap

output:
configure: error: This c-client library is built with SSL support.

      Add --with-imap-ssl<=DIR> to your configure line. Check config.log for details.

So, the configure script is finding the c-client libraries.

Output from config.log:

/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:268: the use of `tmpnam' is dangerous, better use `mkstemp'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:281: undefined reference to `RAND_seed'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:286: undefined reference to `SSL_library_init'
/usr/local/lib/libc-client.a(osdep.o): In function `ssl_start_work':
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:388: undefined reference to `TLSv1_client_method'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:388: undefined reference to `SSLv23_client_method'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:388: undefined reference to `SSL_CTX_new'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:391: undefined reference to `SSL_CTX_ctrl'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:395: undefined reference to `SSL_CTX_set_verify'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:397: undefined reference to `SSL_CTX_set_default_verify_paths'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:398: undefined reference to `SSL_new'
/install/imap-2002a.DEV.SNAP-0212051126/c-client/osdep.c:400: undefined reference to `BIO_new_socket'