he recently detected TRAPPIST-1 planetary system, with its seven planets transiting a nearby ultracool dwarf star, offers the first opportunity to perform comparative exoplanetology of temperate Earth-sized worlds. To further advance our understanding of these planets' compositions, energy budgets, and dynamics, we are carrying out an intensive photometric monitoring campaign of their transits with the Spitzer Space Telescope. In this context, we present 60 new transits of the TRAPPIST-1 planets observed with Spitzer/IRAC in February and March 2017. We combine these observations with previously published Spitzer transit photometry and perform a global analysis of the resulting extensive dataset. This analysis refines the transit parameters and provides revised values for the planets' physical parameters, notably their radii, using updated properties for the star. As part of our study, we also measure precise transit timings that will be used in a companion paper to refine the planets' masses and compositions using the transit timing variations method. TRAPPIST-1 shows a very low level of low-frequency variability in the IRAC 4.5-μm band, with a photometric RMS of only 0.11% at a 123-s cadence. We do not detect any evidence of a (quasi-)periodic signal related to stellar rotation. We also analyze the transit light curves individually, to search for possible variations in the transit parameters of each planet due to stellar variability, and find that the Spitzer transits of the planets are mostly immune to the effects of stellar variations. These results are encouraging for forthcoming transmission spectroscopy observations of the TRAPPIST-1 planets with the James Webb Space Telescope.