3essentials supports IMAP on it's latest web servers. Currently it's available only on web14,web16 and web18. For webservers web12 and below, this option is not available. Customers on those servers who want IMAP support, should contact the billing team (billing@3essentials.com) and inquire about upgrading your hosting plan to a current plan version which supports IMAP. 

Note: IMAP idle is available only on the web18 and web20 servers.