Comet 49P/Arend-Rigaux is a well known low-activity Jupiter Family comet. Despite the low activity, we have witnessed outgassing activity in 1992, 2004, and 2012. In 2012 a broad tail-like feature (PA ∼ 270°, ∼2.3 × 105 km) and a narrow jet-like feature (PA ∼ 180°, ∼9.3 × 104 km) were seen simultaneously. Using Finson-Probstein (FP) dust dynamical models we determine: the grain sizes released in each event; the duration of activity; when the activity peaked; and the velocity of the dust particles, allowing us to make comparisons between the events. We find that the tail feature in 2012 is similar to the tail in 1992 with large grains (40-4000 μm) peaking in activity around perihelion with a long duration of outgassing greater than 150 days. The jet feature from 2012, however, is more similar to the 2004 event which we model with small grains (1-8 μm) with a short duration of activity on the order of one month. The main difference between these two features is that the 2004 event occurs prior to perihelion, while the 2012 event is post-perihelion. We use the grain sizes from the FP models to constrain ice sublimation models. Between 1985 and 2018 we cover six apparitions with 26 nights of our own observations, data from the literature, and data from the Minor Planet Center, which together, allow us to model the heliocentric light curve. We find that the models are consistent with H2O ice sublimation as the volatile responsible for driving activity over most of the active phases and a combination of H2O and CO2 ices are responsible for driving activity near perihelion. We measure the fractional active area over time for H2O and discover that the activity decreases from an average active area of ∼3% to ∼0.2%. This clear secular decrease in activity implies that the comet is becoming depleted of volatiles and is in the process of transitioning to either a dormant or dead state.