  In this work, we suggest that the intriguing repeating fast radio bursts
(FRBs) are produced by the intermittent fractional collapses of strange star
(SS) crust induced by refilling of accretion materials from its low-mass
companion. Coherent radio emissions are released along the open field lines of
the magnetosphere at a distance of roughly 100 times that of SS radius. Its
periodic/sporadic/clustered temporal behaviors could be well understood in our
scenario. Especially, the periodicity is attributed to the modulation of
accretion rate through the disk instabilities (e.g., thermal-viscous
instability). To account for a $\sim 16$-day periodicity of the repeating FRB
source 180916.J0158+65, a Shakura-Sunyaev disk with a viscosity parameter of
$\alpha \simeq 0.004$ and an accretion rate of $\simeq 3 \times
10^{16}$~g~s$^{-1}$ in the low state is invoked. Monitoring the face-on
low-mass X-ray binaries is strongly encouraged for future repeating FRB
searches. Our scenario, if favored by future observations, will serve as
indirect evidence for the strange quark matter hypothesis.
