  Most ultra-luminous X-ray sources (ULXs) are now thought to be powered by
stellar-mass compact objects accreting at super-Eddington rates. While the
discovery of evolutionary cycles have marked a breakthrough in our
understanding of the accretion flow changes in the sub-Eddington regime in
Galactic Black Hole Binaries, their evidence in the super-Eddington regime
remained elusive. However, recent circumstantial evidence had hinted the
presence of a recurrent evolutionary cycle in two archetypal ULXs: Holmberg II
X-1 and NGC 5204 X-1. Here we build on our previous work and exploit the
long-term high-cadence monitoring of Swift-XRT in order to provide evidence of
the evolutionary cycle in these two sources and investigate the main physical
parameters inducing their spectral transitions. We study the long-term
evolution of both sources using hardness-intensity diagrams (HID) and by means
of Lomb-Scargle periodograms and Gaussian processes modelling to look for
periodic variability. We show that both sources follow a recurrent evolutionary
pattern in the HID that can be characterized by the hard ultraluminous (HUL)
and soft ultraluminous (SUL) spectral regimes, and a third state with
characteristics similar to the supersoft ultraluminous (SSUL) state. The
transitions between the soft states seem aperiodic, as revealed by timing
analysis of the light curve of Holmberg II X-1, albeit further investigation is
warranted. The light curve of NGC 5204 X-1 shows a periodicity of $\sim$ 200
days, possibly associated with the duration of the evolutionary cycle. We
support a scenario in which the spectral changes from HUL to SUL are due to a
periodic increase of the mass-transfer rate and subsequent narrowing of the
opening angle of the supercritical funnel. The narrower funnel, combined with
stochastic variability imprinted by the wind, might explain the SUL--SSUL
spectral changes.
