The style of subduction that prevailed on the early Earth, or even whether subduction was prevalent at all, is an important question in the evolution of Earth's crust, mantle, and surface environment. Here, two-dimensional numerical convection models, that include grain size evolution to generate weak plate boundaries, reveal a clear transition in subduction behavior with increasing internal heating rate. Sustained subduction with a coherent slab gives way to a style where slabs periodically detach and sink rapidly into the deep mantle, with increasing internal heating rate. In this latter, "drip-like" subduction regime, repeating cycles of slab growth by subduction, followed by necking and detachment of the lower portion of the slab, are seen. These cycles are termed "slab detachment cycles," and similar behavior has been seen in regional scale subduction models of the early Earth. Fourier analysis is used to constrain the timescale of slab detachment cycles, and a simple scaling law for this timescale is developed. Applying the scaling law to the early Earth indicates that slab detachment cycles can occur on timescales of <10 Myr, even as low as <5 Myr if the lithosphere is thick and mantle temperature is >1900 K. These cycles may thus be capable of explaining repeating sequences of rocks with "arc" and "non-arc" signatures seen in some Archean cratons. The drip-like subduction regime could also have significant implications for the generation of the tonalite-trondhjemite-granodiorite (TTG) suite of rocks and exhumation of high pressure metamorphic rocks, two important features of the early Earth geologic record.