Determining the energy dependence of fusion cross sections at extremely low energies is crucial for various astrophysical processes. In the previous study by Jiang et al. [Phys. Rev. C 75, 015803 (2007)], it was concluded that fusion cross sections for the $^{12}\mathrm{C}+^{12}\mathrm{C}$ system rapidly drop off as the energy decreases. We here reexamine this hindrance phenomenon. While the previous study fitted the logarithmic slope $L(E)$ of fusion cross sections with a function of $L(E)=A+B/{E}^{n}$ and sought the optimum value of $A$ and $B$ with $n=1.5$, we refit the data with the same function for $L(E)$ but by releasing the restriction on $n$. We find that the optimum values of $n$ significantly deviate from $n=1.5$. For the $^{12}\mathrm{C}+^{12}\mathrm{C}$ system, the presence or the absence of the hindrance phenomenon depends on a fitting procedure and a selection of data sets. On the other hand, for the $^{12}\mathrm{C}+^{13}\mathrm{C}$ system, we show that the optimum values of $n$ are smaller than $n=1.5$ regardless of the details of the fitting procedure, indicating the absence of hindrance in the fusion cross sections.