Abstract Experiments of non-premixed combustion in micro-channels have exhibited different modes of burning. Typically, a diffusion flame is established along or near the axis of a channel spanning the entire mixing layer. It separates a region of fuel and no oxidiser from a region with only oxidiser. Often, however, a periodic sequence of extinction and reignition events, termed collectively as “diffusion flame-streets”, are observed. They constitute a series of separate diffusion flames, each with a tribrachial edge flame structure that is stabilised along the channel. The current work focuses on understanding the underlying mechanism responsible for these unique observations. Numerical simulations were conducted in a thermo-diffusive limit to examine the effects of confinement and heat loss on flames in three dimensional micro-channels with low aspect ratios. An asymptotic analysis was used to reduce the mathematical equations into a two-dimensional problem which effectively captured the three dimensional nature of the combustion process. Two key burning regimes were identified: (i) stable continuous diffusion flames and (ii) stable diffusion flame-streets. The transition between regimes is demarcated primarily by the Damkohler number, defined as the ratio of a diffusion time to a chemical reaction time, but is also influenced by the extent of heat loss. Occasionally within the diffusion flame-street regime, the residual mixture would reignite but would fail to evolve into stationary auxiliary flames. This was generally observed at low flow-rates for Reynolds numbers below a critical value. The behaviour appeared to be periodic in time with a frequency that depended on the removal from criticality.