Startups innovate under extreme uncertainty and time pressure, creating a continual need for guidance across discovery, experimentation, and early product decisions. Human coaching can foster reflective learning and problem framing, but it is intermittent, capacity-constrained, and offers limited day-to-day visibility into venture work. Meanwhile, founders increasingly use LLM-based assistants, yet current tools are generic, overly affirmative, and poorly aligned with coaching goals because they lack persistent venture context, workflow continuity, and explicit agency boundaries. This paper contributes design-relevant knowledge of the problem space for AI-based entrepreneurial coaching systems. Drawing on interviews with startup founders and coaches in Germany, we explicate recurring breakdowns in current coaching and tool support and derive four empirically grounded design requirements: (1) task-oriented venture progression support, (2) structured venture building, (3) assumption-driven learning and validation, and (4) reflective and developmental support that preserves founder agency. We discuss design tensions, boundary conditions, and an agenda for evaluating AI coaching as scaffolding rather than substitution.