A 2-cm electron cyclotron resonance ion source has the advantages of long life and high specific impulse, which can meet the requirements for space gravitational waves detection. In the experiment on finding the lower limit of thrust, it is found that when the ion source operates under the extreme condition of 0.5-W microwave power and 0.1-sccm gas flow rate, increasing the voltages of grid system excessively may cause flameout. The plasma discharge level is controlled by the gas supply, microwave, and power supply system, and their small disturbances will make experimental results different, thus the flameout of the ion source appears randomly and transiently. Besides, it is difficult to observe the flameout phenomenon experimentally, because the probe diagnosis has big interference to low-density plasma, and the optical diagnosis is blocked by the grid system. Therefore, the integrative simulation with the full particle-in-cell method is used to simulate the operating process of the ion source, whose calculation range includes the discharge chamber, grid system, and plume. Through simulating the processes of plasma discharge and ion beam extraction continuously in space and time, the flameout phenomenon can be reproduced artificially after increasing the voltages of grid system. The simulation results show that the ambipolar diffusion between the antenna and discharge chamber is the fundamental reason for the flameout of the ion source. In the circuit, the antenna does not touch the discharge chamber but for bulk plasma, which makes its surface gradually accumulate charges until it reaches the floating potential. Because the increase of the voltage of antenna lags behind that of grid system, a strong electric field will appear between the antenna and chamber. Then, electrons and ions respectively move toward the chamber and antenna, the ambipolar diffusion helps the antenna reach the floating potential rapidly. When the plasma density inside the chamber is low, the ambipolar diffusion will cause flameout. In order to avoid the flameout of the ion source in such an extreme situation, an improvement measure that the voltage of antenna equals the voltage of chamber is proposed, which is verified by the integrative simulation. The study on the flameout phenomenon will provide a theoretical basis for the design and application of the ion source, which can help the ion source operate safely to meet the requirements for space gravitational wave detection.