Considering that democracy was achieved through substantial efforts.
I'd first question your use of the term "moral" in this context. Most modern concepts of "morality" entail universality. They attempt to transcend the historical and conditional. The "nation-state," democratic or not, is not, by definition, a universal state... and thus not in itself a source of "moral" obligation.
I would also question your rationale, "considering that democracy was achieved through substantial efforts." One could say the same of almost any government. Even hereditary kings must sit uneasily upon the "throne of bayonets." The Third Reich was an outcome of considerable effort, much of it "democratic" in form.
In addition, the term "democracy" has many different definitions and electoral forms. In the newly founded United States, for example, perhaps only one-fifth of the adult working population was legally enfranchised. In certain phases of Marxism, on the other hand, national elections and parliamentary systems were abolished as too centralized, abstract, and prone to corruption, while workers in the early "soviets" could vote on work and management issues directly affecting them. In ancient Athens, ideally, "representative" government was not thought "democratic," and citizens voted on everything and rotated through public offices.
Finally, I think it is easy to imagine scenarios in which not voting could be a "moral" act of civil dissent. Most nation-states, no matter how despotic, have official elections of some sort. A referendum legitimizes power and, in advanced countries, gives a compensatory sense of popular participation, somewhat like "commenting" on internet sites. There may be cases where assent to narrow, false, or corrupted choices may not be the highest moral act.
One can construct a reasonably strong argument that voting is a moral obligation for a citizen in a democracy, but whether that argument is cogent or not depends on a number of premises that not everyone accepts.
The first variable is what moral system we're evaluating this question by. Let's assume a basic utilitarianism for purposes of the illustration --it makes the argument simple: If the full utilization of suffrage brings the greatest good to the greatest number, then yes, every citizen has a moral duty to vote.
That premise is far from certain, however. At the least, I'd think you'd want to qualify it to state that the moral duty is to vote in a well-informed manner --the appeal of a charismatic tyrant to the uninformed masses has been a major complaint against democracy dating back at least as far as Plato. You would also need to consider scenarios such as well-informed abstention (when all available choices are undesirable), as well as the basic question of whether participating in democracy is always better than making moves towards establishing some alternate form of governance. Finally, there's the question of what form of democracy is being referenced. Very few places rely on actual direct democracy --is it still an obligation to vote under a system where voting is largely symbolic?