atmc.net incompatibility with MAC Mail in Mountain Lion in Holden Beach, NC

within last 2 weeks (July 2013) after latest OS security update, my local provider ATMC.net can not provide email connection to my iMac. Previously worked ok for 2 years. ATMC (Shallotte, NC) tech support and 2nd level tech support could not fix the problem. They suggested exchanging the ATMC provided DSL modem/router (current device less than 1 year old). Any ideas for solving this problem

Thanks, Rod