Hello Anonymous,
I would suggest if the company is focused on this specific criteria, then you should refrain from attending its interview process again, else no other thing should stop you form at least to attend. Sometimes, the companies put a disclaimer on the same and are very strict on these lines. But, in my experience I have seen one of my friends who was rejected at a certain off-campus interview of some company, was again eligible to sit of the interview process again after one month. Although he flunked again in the same but, that did not stop him from keep on trying, even though people kept on telling him that he would be disqualified and blah this and blah that. He went ahead, registered once again and then gave the interview.