When I first started focusing on short stories, I submitted to a range of top professional magazines (Clarkesworld, Strange Horizons, etc.). I wasn't surprised to be rejected, but now I wonder if after rejecting a few pieces from me, they will attach a negative note or connotation to my name that could hurt future submissions. Obviously I don't/won't submit work that I don't think is ready for the world, but hopefully my future work will become increasingly better. Is there a benefit to holding off top-tier submissions until some time in the future?
No, don't hold stories back unless you have a specific reason. Unless a publication specifically asks you to re-submit a specific piece at a later time (maybe they have a theme issue planned), holding stories back makes little sense. There's no secret to getting published aside from (1) Write beautiful things (2) send the beautiful things to publications that things like the things you wrote. (i.e., send to appropriate markets and follow their submission guidelines.)
The stories that you send in should be the best you're capable of at that time. Why would you hold work back unless you think it's not ready? By saving top-shelf material for later, you'll all but ensure that you're not giving your best stories a chance to be noticed. And it's expected that writers will improve over time.
If you were rejected with a form letter, they may not even remember you. If you were rejected with a personalized note, it's because they want to encourage you. If you send in a better story later, and they remember you, they'd almost certainly love to see that you've improved.
Absolutely not. Getting rejected is all part of the business. Just because they don't like one - or maybe several - of your stories doesn't mean they won't find one that they love in the future. Keep submitting and keep dreaming. You'll get there in time.