That helps to clarify. Generally, HR online systems reset their applications around once a year, some do it more often as positions are posted and released, but usually not longer than that. Your email and account may still be in their system, but your previous application will likely be inactive or deleted by that time.
Going back to reapply to a firm definitely shows you are very interested, but it probably also depends on why they did not offer you a position the first time around. If it was for a lack of cultural fit, then another year of experience is unlikely to help; however, if it was just a decision on some other factors (i.e. had to cut someone out of a pool of qualified applicants), then reapplying will definitely be a good way to demonstrate strong interest.
Back to your question, probably not sooner than 1 year as that is the typical recruiting cycle and also gives you a chance to show how your profile/candidacy has improved during that time, but perhaps longer. Are you only able to get interviews with the same firm? Unless you have some sort of crush, there are 3 other firms that will give your career a similar boost. In any case, I elaborated on things you didn't ask but just wanted to throw some thoughts your way. I hope this helps. Good luck!
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