Critically discuss if government intervention to alleviate poverty are sustainable over a long period of time

Since you didn't specify what government you mean specifically, I will make a more abstract comment - often when governments try to alleviate poverty, their interventions and reforms are sustainable. That's because governments have the power to make structural changes, such as to improve literacy or education, which would have long-lasting effects on eradicating poverty. So at least in theories, yes, the governments have such a possibility and their efforts can be sustainable.

That would be true i believe