We report on temperature-dependent soft X-ray absorption spectroscopy (XAS) measurements utilizing linearly polarized synchrotron radiation to probe magnetic phase transitions in iron-rich Fe1+yTe. X-ray magnetic linear dichroism (XMLD) signals, which sense magnetic ordering processes at surfaces, start to increase monotonically below the Neel temperature TN = 57 K. This increase is due to a progressive bicollinear antiferromagnetic (AFM) alignment of Fe spins of the monoclinic Fe1+yTe parent phase. This AFM alignment was achieved by a [100]-oriented biasing field favoring a single-domain state during cooling across TN. Our specific heat and magnetization measurements confirm the bulk character of this AFM phase transition. On longer time scales, however, we observe that the field-biased AFM state is highly unstable even at the lowest temperature of T = 3 K. After switching off the biasing field, the XMLD signal decays exponentially with a time constant {tau} = 1506 s. The initial XMLD signal is restored only upon repeating a cycle consisting of heating and field-cooling through TN. We explain the time effect by a gradual formation of a multi-domain state with 90 deg rotated AFM domains, promoted by structural disorder, facilitating the motion of twin-domains. Significant disorder in our Fe1+yTe sample is evident from our X-ray diffraction and specific heat data. The stability of magnetic phases in Fe-chalcogenides is an important material property, since the Fe(Te1-xSex) phase diagram shows magnetism intimately connected with superconductivity.