The main aims of this paper are to study the influence of the Gestation Age (GA) on the quality of recorded abdominal ECG (aECG) signals and to evaluate the performance of the LMS and RLS adaptive signal processing algorithms in the extraction of the fetal ECG (fECG) signal component from such signals. This influence is quantified as a function of the Signal-to-Noise Ratio (SNR). Our research shows that these adaptive algorithms with optimized settings can successfully be applied to extract fECG signals from the maternal aECG signals as early as the 30th week of GA, hence addressing a limitation (37 weeks or labor) in commercially available monitoring systems. We demonstrate that before this gestational age, the SNR of the maternal aECG signal is too low for these adaptive algorithms to work effectively and produce satisfactory results.