The Hilbert–Huang transform (HHT) has been used as a powerful tool for analyzing nonlinear and nonstationary time series. Soil loss is controlled by complicated physical processes and thus fluctuates with nonlinearity and nonstationarity over time. In order to further clarify the relationship between rainfall, surface runoff, and sediment yield, this study adopted the HHT to analyze these characteristics through multiple time scales and investigated their relationship through time-dependent intrinsic correlation (TDIC) in the time series. A six-year study (2015–2020) was conducted on sloping farmlands to explore the relationships between soil loss and rainfall in southwest China. Time series of soil loss and rainfall were identified as the relevant characteristics at different time scales based on the method of HHT. Local correlation between the soil loss and runoff was carried out by the method of TDIC. The original time series of the rainfall, runoff, and soil loss were decomposed into eight intrinsic mode functions (IMFs) and a residue by ensemble empirical mode decomposition (EEMD). The residue indicated that the rainfall and runoff increased and then decreased during the maize-growing season from 2015 to 2020, whereas the soil loss gradually decreased. IMF1 and IMF2 accounted for nearly 80% of the temporal variations in rainfall, runoff, and soil loss, indicating that the variables varied the most at short time scales. The TDIC analysis showed that strong and positive correlations between the soil loss, rainfall, and runoff prevailed over the entire time domain at the scales of IMF1 and IMF2, indicating the rapid response of the soil loss to rainfall and runoff at short time scales. Time-varying correlations were observed at the IMF3–IMF5 scales. At the IMF7 scale, an evident switchover in the nature of the correlation was identified during the years 2018 and 2019; this could be related to a sudden rainstorm under low vegetation coverage conditions. The EEMD-based TDIC tool is an effective means to clarify the relationship between soil loss, rainfall, and runoff. Our results provide a better understanding of the relationship between soil loss and rainfall varied with time at multiple time scales. Short-term heavy rainfall and rapid surface runoff are the important factors causing serious soil and water loss on a short time scale in a mountainous region with yellow soil, which is of great significance for the construction of a regional soil erosion prediction model.