We study the strong coupling behaviour of 1/4-BPS latitude Wilson loops in the N=4 SYM theory, computing the one-loop corrections to the relevant classical string solution in AdS5xS5 in sigma-model perturbation theory. The approach is based on the application of the Gel’fand-Yaglom method to compute the functional determinants for the fluctuations of the type IIB Green-Schwarz action expanded around the minimal-area surface. We normalize the vev of the Wilson loops with respect to the 1/2-BPS circular case to circumvent the problem of determining the overall constant contribution from the normalization of ghost zero modes. We find a discrepancy with the result obtained via localization in the gauge theory, and we discuss some issues that might be responsible for this outcome of the one-loop analysis.