It's not gmail that connects with the phone, it's the phone that connects with gmail. In fact, it's not even the phone, it's the e-mail program that does it. Common programs for that on an Android phone are the browser (Chrome) or the gmail app, or any other mail app you installed.

Now suppose that you used one of 10 "best mail apps" from http://www.androidauthority.com/best-android-email-apps-579368/, then you shouldn't contact Gmail nor Samsung, but the customer support of that app.
In fact, it could be that switching to such a different program is a solution (not necessarily the best or easiest) to your connection issue.