The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which-if uncorrected-will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction(1-9), the carrier of the information can also be completely lost or the information can leak out of the computational space(10-14). It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code(15,16) in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary qubit, which acts as a minimally invasive probe that detects absent qubits while imparting the smallest quantum mechanically possible disturbance to the remaining qubits. Upon detecting qubit loss, a recovery procedure is triggered in real time that maps the logical information onto a new encoding on the remaining qubits. Although the current demonstration is performed in a trapped-ion quantum processor(17), the protocol is applicable to other quantum computing architectures and error correcting codes, including leading two- and three-dimensional topological codes. These deterministic methods provide a complete toolbox for the correction of qubit loss that, together with techniques that mitigate computational errors, constitute the building blocks of complete and scalable quantum error correction.