  For applications of solid state quantum computing and quantum simulations,
high fidelity initialisation of thermally mixed electronic and nuclear spin
qubits is essential. Whereas electronic spins can readily be initialised
optically to high fidelity, initialisation of the nuclear spins requires
alternative approaches, such as dynamic nuclear polarisation (DNP) via the
electronic spin. Pulse-based DNP methods, such as PulsePol, are already widely
utilised. By means of repeated application of PulsePol sequences, interspersed
with re-initialisation of the electronic spin, high levels of nuclear
polarisation -- termed hyperpolarisation -- have been achieved. From
theoretical analysis of these protocols perfect nuclear initialisation is
expected; however, in practice, saturation below $\sim$ 95$\%$ is seen in
experiment. We develop an analytical model to describe hyperpolarisation
dynamics, predicting non-maximal nuclear polarisation saturation in the
asymptotic limit for realistic nuclear spin clusters. We argue that perfect
initialisation of a typical nuclear cluster using this method may not, in
general, be possible even with an arbitrarily large number of repetitions.
