  The search for novel phases of matter is a central theme of modern physics,
with some of the most intriguing examples provided by the spin liquids found in
magnets with competing, or "frustrated" interactions. Ca$_{10}$Cr$_7$O$_{28}$,
a novel spin-$1/2$ magnet with a bilayer breathing-kagome lattice, has
properties which differ from from any known spin liquid. However, understanding
Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because of its
complex frustration. Here we use large-scale molecular-dynamics simulation to
explore the origin of spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$. We
uncover qualitatively different behaviour on different timescales, and argue
that ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a
slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the
U(1) spin liquid found in the kagome antiferromagnet. These results provide a
concrete scenario for spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, and
highlight the possibility of spin liquids existing on multiple timescales.
