I would argue that no, the Weimar Republic was not bound to fail, but it did have the odds stacked against it, and was unlikely to ever be particularly "successful". Moreover, if Weimar Germany wasn't bound to fail, interwar Europe probably was.

It's difficult to argue this sort of point without delving into counterfactual history, but I'll do my best.

To being with, I'd say that it is not so much the events of World War I and the postwar settlement (ie the Treaty of Versailles) that one must contend with when considering the fate of the Weimar Republic. Both the terms of the treaty--which stripped Germany of territory in Europe, all its colonies, imposed restrictions on the size of its military, and demanded immense reparations payments--as well as the manner in which it was negotiated and imposed on Germany made the treaty incredibly unpopular and thus an easy target for the myriad of nationalist political parties that emerged in the interwar period.

It's also important to remember that some of the Weimar Republic's internal struggles were self-imposed. The hyperinflation of the 1920s--which saw the value of cash money plummet so rapidly that Germans were rushing to spend their paychecks as quickly as possible and prices increasing a million-fold--was largely a product of currency manipulation within the German government to avoid repayment of reparations.

In this context, the political structure of the Weimar Republic did not help matters. For one thing, although the German Empire that preceded the Republic (which, technically, was still known as the German Empire) had featured an elected parliament (the Reichstag), the existence of such a body prior to 1919 did nothing to prepare German politicians for the rigors of actually running a government. You see, under the Kaiser, the Reichstag was a glorified debating club, with extremely limited ability to affect policy. Germans didn't go into politics to affect governing--to do that, you'd go into the bureaucracy. Rather, Germans in the Reichstag debated and voted but beyond budgets had limited impact--and even when it came to budgets, the impact was limited. Because debates and votes were thus of little real consequence, there was little motivation to compromise, because all that would do was alienate voters without actually achieving anything. Thus, after 1919, a generation of German politicians showed up for work with no experience actually governing and a great deal of experience not compromising.

To make matters worse, the proportional representation system implemented in the Reichstag resulted in the proliferation of small political parties representing niche interests, making it even more difficulty to put together enough votes to pass legislation. These parties represented a substantially expanded electorate, which now included women and many more men than before. But Germany was by no means the worst off in this regard; some European states had 18+ political parties in parliament.

Still, like other European states, the new Weimar Republic was on the one hand a nascent republic, a fledgling democracy with little experience, and on the other hand trying to do a great deal all at once; across Europe the new constitutions written after World War I promised not just basic civil liberties and rule of law but social welfare programs. These made the task of governing even more difficult.

Perhaps the biggest obstacle, however, was dissatisfaction with the new political system. When the first elections to the Reichstag were held, some 25% of the representatives elected came from parties opposed to the Republic in some way or another, either on the left or the right. The Weimar Coalition, made up of the Catholic Center Party, Social Democratic Party, and the German Democratic Party, disagreed on many issues, but at least the agreed on the basic form and function of government, democratic representation, etc. Most other parties wanted the new constitution replaced with some other form of government, whether communist, monarchist, or what have you.

And support for the parties in the Weimar Coalition waned over time. Remember, already in 1919 25% of voters supported anti-Republican parties, and that number increased over time, largely from dissatisfaction as the government seemed incapable of fixing problems.

Except it wasn't incapable, especially as the 1920s progressed, and even leaders from parties originally opposed to the Weimar Coalition, like Gustav Stresemann, proved themselves capable of navigating the Republic through crises, negotiating new payment plans for reparations, easing tensions between Germany and France, and more. Stresemann only served as Chancellor for a short time, but had he not died a few years later of a stroke, perhaps his party would not have returned to its more anti-Republican stance.

The efforts of Stresemann and others to save the Republic again and again, even going so far as to invoke emergency powers without using them to dismantle the republic (as Hitler would later do), suggests to me that the Republic was not doomed. However, the global Great Depression hit Germany hard, and made it possible for parties like the NSDAP and their charismatic leader, Adolf Hitler, to turn people further against the republic in search of new solutions. If it hadn't been Hitler, another leader would have risen to lead the Nazis; if it hadn't been the Nazis, another right-wing party would have made similar attempts.

Most importantly, though, I think that while the Weimar Republic was not necessarily bound to fail, it was never going to be particularly strong, either. Which is important, because even if Germany hadn't provided the impetus for things in the late 1930s, something would have.