I would say that it is always important for people to validate and approve their Constitution. In the case of the fledgling nation struggling to exist, the validation of a people in embracing their new constitution helps to give legitimacy to both the nation as well as the governing body that has constructed the constitution. If a group of people saw the enforcement of a constitution as a delegitimate process or document, there could be a massive destabilization of the new government. Over time, I also think it is importance for, perhaps not approval, but a sense of public belief and faith in the constitution. A nation becomes more progressive and more refined in its pursuit of natural political ends when it feels comfortable with its founding document of codified laws and practices. The United States might be an example of this. Over time, the Constitution has abolished slavery, established rights for women and people of color as well as young people, identified fiscal policy, and dictated the limitations of presidential succession, amongst other elements. This has only been able to be done because people, Americans, felt comfortable enough with their document to give it their voice of approval in making modifications to it.
In many ways, it is irrelevant whether the populace approves of the constitution or not, as long as the powerful forces that will be running things can come to some agreement, the popular agreement is sought really only to be sure to keep them under control.
Ideally, it would be vital for a group of people being governed by a document to approve of it, but it is impossible for small groups of people to completely agree, and even more impossible for nations of people to do so.
So I would say that superficially it can be important to have some agreement. Underneath it all, it only matters that the folks with the power buy into it.
Well, it's only important if it's the Constitution of a democracy, and then it's only important that a majority of the people approve of it. Government of any kind is as imperfect as the humans that create it, so it is impossible to ever garner total support for a governing document like a Constitution.
Plus, let's look at the purpose of a Constitution - to establish a legal framework for a functioning government. Even if 40% of a population disapproved of a Constitution, wouldn't they disapprove more strongly of having no government at all? Lack of support is relative in this case, as it often is in democracies.
Another thing to keep in mind here is that not everyone is going to agree and approve of the Constitution. Like the previous responder said, the Constitution here in the United States has been around for so long that none of us were here when it was written, yet it works so we keep it. Everyone is going to have differences in opinion and think that certain parts to be changed but that is inevitable.
When a constitution is new it is often changed so that it works better. In this case it is important that it is approved by the majority. In this sense, the people feel that the constitution is for them as individual people and then take pride in it.
In my opinion, it is not all that important once the Constitution is well established. For example, here in the United States, the Constitution has been around for so long that none of us living today had anything to do with approving of it. There are surely parts of it that many of us disagree with or things we wish were in it. But because it has worked well for the country in the past, we respect it and pretty much obey it.
However, when a constitution is new, it is very important that it be democratically created and approved. This is important because it gives the people the sense that the Constitution belongs to them. It is not something that has been imposed upon them by some outside force. This makes them more likely to respect it and it makes the nation much more likely to be stable.
I should say, however, that this is not completely true. The Japanese had their consitution imposed on them by the US occupation after WWII. Even so, their constitution is still used and their nation is stable. So it is not necessary for the constitution to be democratically approved.