I think, in regard to this question, it's best to view the French Revolutionary Wars and the Napoleonic Wars in the greater context of European history and the balance of power of the European states.

If we start in the post-religious wars era in France, we can start with Louis XIV (1643-1715). During his reign, the major wars fought by European powers in which France took part included the Franco-Spanish War (1635-59), War of Devolution (1667-8), the War of the Grand Alliance (1688-97), and the War of Spanish Succession (1701-14). Note, that the League of Augsburg from the War of the Grand Alliance (which included most European powers except France and persisted in some form until the War of Austrian Succession) was formed at least partially to stem Louis XIV's expansionist tendencies in Europe. I would say that France was generally successful in these wars as they didn't lose any war outright and came out with a net gain of territory, though it wasn't much.

Under Louis XV (1715-74), the major European wars included the War of Austrian Succession (1740-8) and the Seven Years' War (1755-64). France did not make out as well in these wars, losing territory to the British in the New World (territory east of the Mississippi) and in India. It also put a heavy financial strain on France, which helped lead to the Revolution.

It's important to look at this history because it shows that, during this era, Europe was at war very often and a string of losses was usually not enough to deter a great power from going to war again. The numerous coalitions formed against the Republic and Napoleon because, in general, it was common for European powers to go to war at this time and France in this era embarrassed the other powers.

From the First to Fifth Coalition Wars, France won vast expanses of territory in Europe from other powers. At the Empire's height, it had direct control of France, the Low Countries, portions of Italy, Illyria, and Catalonia. It had indirect control (usually in the form of one of Napoleon's relatives ruling, which was also embarrassing for other powers) over Spain, the rest of Italy, West Germany (the area around the Rhine), and the newly formed Duchy of Warsaw. Finally, Napoleon basically made client states out of traditional powers like Austria, Russia, Denmark, and Prussia.

In all, the numerous coalitions formed because it was common for European powers to be at war during this time period. They formed against France, even though France won numerous wars against them, because France won large swaths of territory from other powers and embarrassed them by removing their kings (Spain), stripping away territory to make new states (Prussia), and completely abolishing them as states (Holy Roman Empire).