We propose a quantum-resistant quantum teleportation (QRQT) framework protected by post-quantum cryptography (PQC) to secure the classical correction channel, which is vulnerable to quantum adversaries. By applying PQC to the classical control bits, QRQT eliminates the classical attack surface of quantum teleportation. Our analysis reveals that quantum memory is a hidden bottleneck linking physical and computational security: its finite coherence time simultaneously limits communication distance, constrains tolerable PQC overhead, and restricts the adversary attack window. Under realistic parameters (1 ms coherence, fiber-optic propagation), the maximum secure teleportation distance ranges from 191 km (FrodoKEM-1344) to 199 km (Kyber512). We show that the joint classical-quantum attack probability exhibits a non-monotonic, Bell-shaped profile due to the opposing time dependencies of classical cryptanalysis and quantum decoherence, establishing a bounded optimal attack window beyond which adversarial success decays exponentially. We further analyze how leakage of classical correction bits affects teleportation security under four stochastic leakage models: independent exponential, sequential, burst, and correlated leakage, also accounting for amplitude damping on the shared Bell pair. For each scenario, we derive closed-form expressions for the average Holevo quantity and teleportation fidelity as functions of time, providing measurement-independent upper bounds on extractable information and guiding the design of leakage-resilient quantum communication protocols.

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