Abstract: Muon-catalyzed fusion (μCF) uses negative muons to form compact muonic atoms and molecules, thereby reducing the internuclear distance of hydrogen isotopes and enhancing the fusion probability at low temperatures. In the deuterium--tritium system, the formation of the dt\mu molecule followed by rapid intramolecular fusion constitutes the main catalytic cycle. After fusion, however, the outgoing muon may be captured by the produced ⁴He nucleus and form a bound (\alpha\mu)^+ state, thereby leaving the catalytic cycle. This process, known as alpha sticking, is a key microscopic loss mechanism that limits the average number of fusions catalyzed by a single muon and the ideal muon-level energy gain. This work discusses the quantum-mechanical definition of alpha sticking, distinguishes the initial sticking probability \omega_s^0 from the effective sticking probability \omega_s^\rmeff in matter, and reviews the sudden approximation, wave-function-overlap picture, Green's-function Monte Carlo (GFMC), coupled-channel calculations, and tractable T-matrix models. We then incorporate medium reionization, external-field-assisted stripping, resonant muonic-molecule dynamics, and polarization effects into an effective rate-equation framework, and perform a parameterized sensitivity analysis of the dependence of the cycling number X_\mu on the effective cycling rate \lambda_c and the effective sticking probability \omega_s^\rmeff. For the non-polarized benchmark parameters \lambda_c=2.0\times10^8~\rms^-1 and \omega_s^\rmeff=0.004\;5, one obtains X_\mu\simeq148. If the effective sticking probability is reduced and the cycling rate is increased, X_\mu may enter the range of about 200-300. Further improvements based on high-density confinement, external-field-assisted stripping, and resonant muonic-molecule enhancement should be regarded as forward-looking parameterized scenarios whose key parameters require validation by few-body reaction calculations, complete rate-equation modeling, and dedicated experiments. If polarization effects are relevant to the μCF cycle, they should enter the rate equations through the hyperfine population of the initial dt\mu state, molecular formation rates, and reaction-channel branching, rather than through a single phenomenological enhancement factor.