We analyze time crystal effects in a finite system of bosons which form a bright soliton clump on the Aharonov-Bohm ring. In the large particle number limit, N -> infinity, this setup corresponds to the Wilczek model, where it is known that the time crystal behavior cannot be observed in the ground state of the system because a spontaneously formed soliton does not move. Here, we show that while the spontaneous formation of a moving soliton in the ground state can occur for N < infinity, the soliton decays before it makes a single revolution along the ring and the time crystal dynamics is impossible.