imapproxy (SquirrelMail's IMAP Proxy server)

SquirrelMail's IMAP Proxy is a caching IMAP proxy server intended
for use with webmail clients that cannot maintain persistent
connections to an IMAP server.

IMAP Proxy simply sits between your webmail server and your IMAP
server. It accepts connections from your webmail server for each
client login, then proxies that connection to your real IMAP server.
When your webmail client disconnects, IMAP Proxy will leave the
connection open to the IMAP server such that when your webmail client
reconnects, the existing connection may be re-used.