In this paper, we introduce error correction to the Bluetooth Low Energy (BLE) standard by utilising data redundancy provided by the Cyclic Redundancy Check (CRC) code used to detect erroneous packets. We assume a scenario with an energy-constrained transmitter and a constraint-free infrastructure, which allows us to introduce additional signal processing at the receiving side while keeping the transmitter intact. A novel approach of applying iterative decoding techniques to the BLE CRC code is investigated in this work. By using these techniques and real BLE packets collected in an office environment, we show that by enabling CRC error correction, the sensitivity of the BLE receiver can be improved by up to 3 dB. At the same time, up to 60% of corrupted packets can be corrected, which directly translates to a significant reduction in the number of retransmissions and a noticeable energy saving.