Optical clocks are important for precise measurements in the field of physics. As reported, both the instability and uncertainty of optical lattice clocks are more than two orders of magnitude smaller than those of the best microwave clocks. Therefore, in the near future, optical clocks could be used to redefine the second. Nevertheless, an optical clock with reliability comparable to microwave clocks has not been achieved thus far. In this paper, we compared the frequencies of two Ca^+ optical clocks that were nearly continuously operated for 31 days. Through the comparison experiment, the frequency stability of a single clocks was found to be 6.3×10^-18 at an averaging time of 520 000 s and 7.9×10^-18 at averaging time of 262000 s, while the operating uptime rate reached more than 90% in the period of around 5 days. Thus, our experiment demonstrated that it is possible to increase the stability of single-ion optical clocks to the 10^-18 level, while still maintaining quasi-continuous operation with a high operating rate. This result further confirms that optical clocks can potentially be used to redefine the second.