Should the government be allowed to limit their citizens rights during wartime or other hard times that the country is going through? What if it was an apocalyptic event that everyone knew they would die? In what circumstances would the government be able to limit the rights of their citizens?
There's several ambiguities in your question that an answer needs to address. First, I am going to assume that your uses of "should" refer to moral rather than legal determinations. Otherwise, this isn't going to fit under philosophy. Second, I'm going to answer in terms of applied ethics rather than formal ethical theories. Third, I will following your question, use rights language.
Assuming citizens have rights, there are several different ways to conceive of rights. There's Isaiah Berlin's positive and negative rights distinction. On this account, negative rights where the government should not interfere with a course of action. Positive rights reflect those cases where the government or some other party is compelled to act for you. "Keep the government out of the bedroom" articulates a negative right --> to be able to sleep with whom you choose when you choose. "The government should make sure no one goes hungry" is a positive rights claim that the government has a duty to supply everyone with food.
A second distinction some draw is between first-order and second-order rights. A first-order right is something you have a direct right to. A second-order right is something that you have in light of your first order rights. So if you have a first order right to live, then you may claim a second order right that the government give you food. If you have a first order right to speech, then you have a second order right to the means of speaking. (i.e., the government cannot prohibit you from making speeches in public areas if you have a right of free speech). Actually, some take this further and speak of 3rd order rights -- but that's irrelevant for our purposes.
We need one further distinction to complete the philosophical picture. There are absolute and mitigable rights. Absolute rights are those which are of "incomparable worth" (to use a construction from Kant) whereas mitigable rights are those of "price" -- meaning they are tradeable for other things of moral value.
Given these three axes, we can give some answers.
After that it gets a little cloudy mostly because the philosophical pieces break down.
For an absolute positive 2nd order right, it seem possible that some conflict could prevent its execution without being immoral. imagine for instance, a right to paper and printing to build on a right to free expression. Conceivably if the government has no paper, it has lost its ability to perform this right and therewith failed in this right -- but not necessarily morally. (or to put it another way, is it possible for a right to be 2nd order and absolute? Also can there be absolute 2nd order rights? i.e. rights where the government's duty of non-interference is not immediate but is absolute? )
For an absolute positive 1st order right, it would be immoral for the government not to supply but it's difficult to understand what would qualify as such a right.
If a population were to face a situation of certain demise then there would be little scope in tightening a government's hand upon the rights of its citizenry. Yet even in the face of such circumstances it would be the responsibility of each person, as well as the government, to retain a semblance of the civility enjoyed up until that point.
A glance at past scenarios of wartime and disaster period chaos will reveal a great surge in incidences of looting, rape and murder. As the state loses control over order there will be those who will seek to capitalize in vain self-interest.
However there is a wide divide between serving to protect the rights of the people and seeking to limit them for the purpose of retaining control over the populace.
It may be argued that even in a situation of (relatively) non-apocalyptic events such as war, disasters, terrorist threats, and the like, that the limiting of citizens rights serves to subdue the populace and reduce morale (an essential element in facing up to the challenges represented by these circumstances).
Even the expropriation of property - and therefore the limiting of a person's right to enjoy his or her property - is a dodgy move, ethically speaking. It is a sub-ideal choice made in a dire circumstance.
However - it cannot be denied that certain choices having a negative impact upon the rights of individuals may be necessary or at least desirable in gaining advantage in dealing with the crisis (example - expropriation of land for the building of air defenses - or the claiming of crops for rationing purposes) - or the indefinite detaining of persons suspected of intending terrorist acts in detention centers.
The truth that no matter how necessary such measures 'might' be - they represent an erosion in the values practiced by the said government. In conclusion, if the values of the nation are to be valued then there should exist effective checks and balances that prevent a government from limiting the rights of citizens during crisis situations (beyond normal limitations).