The emission of radio waves from air showers has been attributed to the so-called geomagnetic emission process. At frequencies around 50 MHz this process leads to coherent radiation, which can be observed with rather simple setups. Thus, the radio detection technique is used in many experiments consisting in studying extensive air showers. One of them is the Auger Engineering Radio Array (AERA), located within the Pierre Auger Observatory. The frequency band observed by AERA radio stations is 30-80 MHz. This range is highly contaminated by human-made radio-frequency interferences (RFI). In order to improve the signal to noise ratio the filter has to be used to suppress these contaminations, crucial to lower the rate of spurious triggers. The presented filter derived from the Least Mean Squares (LMS) approach can be an potentially new solution instead of the currently in use IIR-notch non-adaptive filter. 32/64-stage filters based on non-canonical FIR filter implemented into cost-effective Altera FPGAs with a sufficient safety margin of the registered performance for the global clock above 200 MHz to obey the Nyquist requirement, proved a very good RFI suppression for typical radio-frequency interferences (RFI) of several mono-carriers for a wide spectrum of fixed learning factors. However, an arbitrary selection of the learning factor in a dynamically changing Argentinean pampas environment may not be optimal. The paper presents a modified algorithm with variable stepsize allowing a dynamically adjustment of the mi factor to changing and potentially new appearing RFI in real AERA environment.