Our email host only allows a small number of connections per IMAP mailbox, however we need 2x the limit number of users to be able to access the account to retrieve mails. Sending isn't required, it's simply reviewing the received mail and deleting/moving to a sub-folder.
Are there any tools available which can sit on a linux server or a Mac desktop and act as a gateway/proxy, so that our host only sees a single connection?
I am not aware of any software that does this by itself; however, might I suggest a multi-faceted approach? I.e., use offlineimap to grab the messages from the IMAP server and put them on your local server, and then use Courier IMAP server to serve them up to your clients. This would give you a single connection to the remote IMAP server (offlineimap), and as many local connections (using Courier) as you would want.
Additionally, since offlineimap supports Maildir, you have plenty of options on how you want to serve it up to your clients.
Good luck!