We present extensive radio observations of the nearby Type Ibc supernovae 2004cc, 2004dk, and 2004gq spanning 8-1900 days after explosion. Using a dynamical model developed for synchrotron emission from a slightly decelerated shockwave, we estimate the velocity and energy of the fastest ejecta and the density profile of the circumstellar medium. The shockwaves of all three supernovae are characterized by non-relativistic velocities of v ~ (0.1-25)c and associated energies of E ~ (2-10) * 1e47 erg, in line with the expectations for a typical homologous explosion. Smooth circumstellar density profiles are indicated by the early radio data and we estimate the progenitor mass loss rates to be ~ (0.6-13) * 1e-5 M_sun/yr (wind velocity 10^3 km/s). These estimates approach the saturation limit (~1e-4 M_sun/yr) for line-driven winds from Wolf-Rayet stars, the favored progenitors of SNe Ibc including those associated with long-duration GRBs. Intriguingly, at later epochs all three supernovae show evidence for abrupt radio variability that we attribute to large density modulations (factor of ~3-6) at circumstellar radii of r ~ (1-50) * 1e16 cm. If due to variable mass loss, these modulations are associated with progenitor activity on a timescale of ~ 10-100 years before explosion. We consider these results in the context of variable mass loss mechanisms including wind clumping, metallicity-independent continuum-driven ejections, and binary-induced modulations. It may also be possible that the SN shockwaves are dynamically interacting with wind termination shocks, however, this requires the environment to be highly pressurized and/or the progenitor to be rapidly rotating prior to explosion. The proximity of the density modulations to the explosion sites may suggest a synchronization between unusual progenitor mass loss and the SN explosion, reminiscent of Type IIn supernovae. [ABRIDGED] ; Comment: 23 pages, 8 figures, 5 tables, accepted to ApJ