The recurrence intervals of slow slip events may increase gradually after a large earthquake during the afterslip. Stress perturbations during coseismic and postseismic periods may result in such an increase of intervals. However, the increasing recurrence intervals of slow slip events are rarely observed during an afterslip. The evolution process along with the afterslip remains unclear. We report an observation of slow slip events following the 2002 Mw 7.1 Hualien offshore earthquake afterslip in the southernmost Ryukyu subduction zone. Slow slip events in 2005, 2009, and 2015 are adjacent to the Mw 7.1 earthquake hypocenter. An increasing slow-slip interval of 3.1, 4.2, and 6.2 years has been observed after the earthquake. We calculated coseismic and postseismic slips from the Mw 7.1 earthquake and then estimated the Coulomb stress changes in the slow slip region. The Mw 7.1 earthquake has contributed positive Coulomb stresses to both the 2005 slow-slip region and 2009/2015 repeating slow-slip region. The coseismic and postseismic Coulomb stress change on the 2005 slow-slip region is approximately 0.05 MPa and 0.035 MPa, respectively. However, both Coulomb stress changes on the 2009/2015 repeating slow-slip region are not over 0.03 MPa. The ongoing afterslip following the Mw 7.1 earthquake last for at least five years, evolving with a decaying stress rate with time. The long-term stress perturbations may be able to trigger the 2005 slow slip event during the afterslip. The 2009 slow slip event seems to be influenced by the afterslip as well. Postseismic stress evolution and frictional and stressed conditions of the slow-slip region can be a reason to affect the evolution process of slow slip events intervals.