Event-driven neuromorphic hardware with on-line learning capabilities enables the low-power local processing of signals on the edge sensors. Implementing such hardware requires having an always-on online learning operation in order to continuously adapt to the changes in the environment. Therefore, as the data is continuously streaming, there cannot be a separation between the training and the testing phase. Such constraint thus asks for a continuous time learning strategy which includes a mechanism to stop changing the weights when the system has reached an optimal operating point, so that it does not over-fit the input data and it generalizes to unseen patterns of the learned class. In this paper we propose spike-based circuits based on a local gradient-descent based learning rule that comprise also this additional “stop-learning” feature and that have a wide range of configurability options over the learning parameters. We describe the circuit behavior and present simulation results for a standard CMOS 180 nm process, showing how the width of the stop-learning region can be controlled along with the learning rate of the system. Such system represents a hardware implementation of a feature which has shown to improves the stability of the learning process and the convergence properties of the network.