A question for your question... Has your port exhibited this behaviour since new, or is this a recent development?
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**Edit**
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Since this problem started after you purchased the machine, it was most likely caused by something getting into the port, or by a physical deformity of the case or connector housing itself. If you can't see anything stuck inside the port, look to see if it is bent/broken anywhere around the edge (mainly right at the top where the cable's clip connects).
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If cables aren't fitting into the port anymore, my workaround would be to make sure you have a cable with lots of slack, and remove the clip that holds it in place. Generally if there is no tension, an ethernet cable will stay in the port without the clip.