The magnetic properties of the two-dimensional dimer spin-gap system SrCu2(BO3)(2) were investigated by the mu(+)SR technique. The relatively slow fluctuations of spin-dimers slow down with decreasing temperature and an unusual spin-freezing process is unraveled at T-f < 3.75 K, well within the spin-gap temperature range (T-SG approximate to 20 K). This quasi-static phase displays a Gaussian field distribution with a remarkable stability with applied longitudinal fields. In support of the criticality of the SrCu2(BO3)(2) spin-gap ground state towards an antiferromagnetic transition, Knight-shift measurements suggest that implanted muons may liberate spin density at T < T-SG that undergoes spin-freezing at very low temperatures. On the other hand, non-magnetic impurity-doping of the copper sublattice does not suppress the spin-gap ground state and does not lead to magnetic ordering effects of static nature.