This type of feedback is frustrating, but it is fairly common. Firms often give feedback at the competency level rather than walking you through every mistake from the interview.
“Consistency in problem solving and communication” usually means the interviewer saw some strong moments, but the performance was not strong enough across the full interview. For example, your structure may have been good initially but weaker later, or your analysis may have been correct but difficult to follow.
Rather than trying to decode every word from the recruiter, reconstruct the interviews yourself. Write down where you hesitated, where the interviewer redirected you, which calculations or exhibits felt weak, and whether your recommendations were concise. Those moments usually tell you more than the rejection call.
If you practiced with strong case partners before the interview, ask them whether they saw the same pattern. It can also help to use a structured approach to asking for feedback after a consulting rejection so you know what to request and how to interpret what the firm gives you. The goal is not to identify one fatal mistake. It is to find the recurring weakness that makes your performance less consistent.