Casual paradoxes are an inherently flawed philosophical concept to begin with. If you go back in time, the most reasonable assumption is that everything that you experienced will continue to be true for you. While you may (in theory) alter the past from everyone else's perspective, that does not mean you can undo the things that motivated you to time travel.
Instead consider that in your own personal perspective, going back in time is just like going forward in time in an uninterrupted series of personal experiences. If this is the case, then causation is not violated.
Consider these three models of time-travel to choose from:
Scenario A - Your older self goes back and co-exists with your younger self. You make a new future for your past self. Because of this he never goes back in time and he experiences a different future than you would have, but his past is not your past; so, you still have the shameful past experience of missing your deadline, while he goes on in ignorance of a future that he will never need to experience.
Scenario B - You become your younger self and re-live your past experiences with the option to make new choices. You fix the mistake yourself, then you go on with your new future, but you still have the shameful past experience of missing your deadline.
Scenario C - You change the past and (then for no reason) your own past rubberbands to account for this. While this is a popular model for science fiction, it would mean that 100% of time travel would create paradoxes. The existence of these paradoxes is actually what rules this out as a realistic expectation of how time-travel would work if it were possible.
In models A & B, what caused you to change the Universal timeline is still true in your Personal timeline. So to answer your question, you probably cannot really stimulate the cause or create an infinite time loop because time-travel would always cause a divergence no matter how hard you try to make it loop. The closest thing to a time Paradox you could have is if you were to follow the B-model of time travel and you continue to go back in time to correct an unfixable mistake or just because you want to experience eternal life, but eventually that person would give up or die in a freak accident; so, at most you could create a long-loop, like someone walking around in circles until they get tired and stop.