  The disc instability mechanism (DIM) is widely accepted to account for the
transient behaviour of dwarf novae (DNe), which experience short outbursts
separated by long quiescence. The duty cycle (the ratio between the outburst
duration and the recurrence time) determines the amount of accreted mass by the
white dwarf (WDs) during outbursts, thus playing an important role in the
long-term binary evolution. Employing the code of Modules for Experiments in
Stellar Astrophysics, we systemically investigate the influence of the duty
cycles on the evolution of DNe and the mass growth of accreting carbon-oxygen
(CO) WDs. Our calculations show that, while the DIM can considerably influence
the accretion process, efficient WD-mass growth requires a particular range of
the duty cycle. For WDs with the initial masses of 0.6, 0.7 and 1.1 $M_\odot$,
these duty cycles are 0.006$\,\leq$$d$$\,\leq$0.007, $d$\,=\,0.005 and
$d$\,=\,0.003, and the accumulated mass of the WDs can reach 0.1, 0.13 and 0.21
$M_\odot$, respectively. In all of our simulations, no CO WDs can grow their
masses to the explosion mass of Type Ia supernovae of about $1.38~M_\odot$.
Because of a much short timescale of the outburst state, the final donor-star
masses and orbital periods are insensitive to the duty cycles. Therefore, we
propose that the DIM in DNe could alleviate the WD mass problem to some extent.
