Internet of Things (IoT) devices are gradually adopting battery-less, energy harvesting solutions, thereby driving the development of an intermittent computing paradigm to accumulate computation progress across multiple power cycles. While many attempts have been made to enable standalone intermittent systems, little attention has focused on IoT networks formed by intermittent devices. We observe that the computation progress improved by distributed task concurrency in an intermittent network can be significantly offset by data unavailability due to frequent system failures. This article presents an intermittent-aware distributed concurrency control protocol which leverages existing data copies inherently created in the network to improve the computation progress of concurrently executed tasks. In particular, we propose a borrowing-based data management method to increase data availability and an intermittent two-phase commit procedure incorporated with distributed backward validation to ensure data consistency in the network. The proposed protocol was integrated into a FreeRTOS-extended intermittent operating system running on Texas Instruments devices. Experimental results show that the computation progress can be significantly improved, and this improvement is more apparent under weaker power, where more devices will remain offline for longer duration.