Kalman Filter - Implementation, Parameters and Tuning
Kalman filters are useful when your input signal consists of noisy observations of some linear dynamical system's state. Given a series of observations of the system state, the Kalman filter aims to recursively provide better and better estimates of the underlying system's state. In order to apply it successfully, you need to have a model for the dynamics of the system whose state you're estimating. As described in detail at Wikipedia, this model describes how the state underlying system is expected to change over one time step, given its previous state, any inputs to the system, and a Gaussian-distributed stochastic component called process noise.

With that said, it's not clear from your question whether you have any such underlying model. The linked post indicated that you're consuming speed values from a sensor. These can be modeled as direct observations of a system's state (where the state is its speed), or indirect observations of its state (where the state is its position, for example). But, in order to use the Kalman framework, you need to choose a model for how that state is expected to evolve as time goes on; this additional information is used in order to generate the optimal estimate. A Kalman filter isn't a magic black box that will just "clean up" a signal that is applied to it.

With that said, the phenomenon that you alluded to, where the Kalman filter will become increasingly confident in its own output to the point where input observations become progressively ignored, does happen in practice. This can be mitigated by manually increasing the values in the process noise covariance matrix. Then, qualitatively, the model for the system's state transition contains a larger stochastic component, so the ability for the estimator to accurately predict the next state given the current state is diminished. This will reduce its reliance on its current estimate of the system state and increase its reliance upon subsequent observations, preventing the "ignoring the input" effect.