A loop reactor (LR), composed as an N-unit loop with step-wise shifted inlet and outlet ports, is one of suggested technological solutions for low-concentration volatile organic compounds (VOC) combustion. Such a scheme ensures a sufficiently high temperature with autothermal behavior and nearly uniform catalytic utilization. The main drawback of the LR is a very narrow window of switching velocities that sustain a stable "frozen" solution that exists if the switching and the pulse velocity are synchronized. In the present work we show the existence of many "finger" -like domains of complex frequency-locked solutions that allow to significantly extend the operation domain, rendering the LR scheme more attractive for practical implementation. A brief comparison with the other heat recuperation technologies (reverse flow and circular loop reactors) is presented.