Some supernovae, such as pair-instability supernovae, are predicted to have a duration of more than a year in the observer frame. To constrain the rates of supernovae lasting for more than a year, we conducted a long-term deep transient survey using Hyper Suprime-Cam (HSC) on the 8.2 m Subaru telescope. HSC is a wide-field (a 1.75 deg2 field-of-view) camera and it can efficiently conduct transient surveys. We observed the same 1.75 deg2 field repeatedly using the g-, r-, i-, and z-band filters with the typical depth of 26 mag for four seasons (from late 2016 to early 2020). Using these data, we searched for transients lasting for more than a year. Two supernovae were detected in two continuous seasons, one supernova was detected in three continuous seasons, but no transients lasted for all four seasons searched. The discovery rate of supernovae lasting for more than a year with the typical limiting magnitudes of 26 mag is constrained to be 1.4-0.7+1.3 (stat.)-0.3+0.2 (sys.)events deg-2 yr-1. All the long-lasting supernovae we found are likely Type IIn supernovae and our results indicate that about 40% of Type IIn supernovae have long-lasting light curves. No plausible pair-instability supernova candidates lasting for more than a year are discovered. By comparing the survey results and survey simulations, we constrain the luminous pair-instability supernova rate up to z ≃ 3 is of the order of 100 Gpc-3 yr-1 at most, which is 0.01-0.1% of the core-collapse supernova rate.