Step 1: Understanding the context
The phrase "despite repeated warnings" suggests that the person did not heed the warnings and failed to meet the expectation of submitting the assignment on time. This indicates a negative outcome, so the verb should reflect that.
Step 2: Analyzing the options
Option (A) "failed" is the most appropriate choice. It suggests that the person did not complete the task despite the warnings.
Option (B) "managed" and (C) "succeeded" imply a positive result, but these do not fit with "despite repeated warnings," which suggests failure to act appropriately.
Option (D) "insisted" doesn’t logically follow, as the person’s insistence wouldn’t necessarily result in the submission on time, particularly after warnings.
Thus, the correct answer is: (A) failed.