Why were the various countries involved in the coalitions weak enough that they lost multiple wars, yet strong enough that they could come back to fight again?
you've asked two questions here; i'll address the one in the title.
the various coalitions formed against Revolutionary and Napoleonic France are not unique. it is perhaps not surprising that only a century earlier a similar series of alliances were repeatedly formed against the preeminent power in Europe at the time--the France of King Louis XIV.
Louis XIV fought 3 major and 2 minor wars during his long reign (1643-1715), all against varied alliances of his European enemies:
| War | France and Allies | Coalitions |
|---|---|---|
| War of Devolution 1667-68 | France | Spain |
| Dutch Republic | ||
| England | ||
| Sweden | ||
| Franco-Dutch War 1672-78 | France | Dutch Republic |
| England (1672-74) | England (1678) | |
| Sweden | Spain | |
| Munster | Holy Roman Empire | |
| Cologne | Prussia | |
| Denmark-Norway | ||
| War of the Reunions 1683-84 | France | Spain |
| Holy Roman Empire | ||
| Genoa | ||
| Nine Years' War / War of the Grand Alliance / War of the League of Augsburg 1688-97 | France | Dutch Republic |
| England | ||
| Scotland | ||
| Holy Roman Empire | ||
| Spain | ||
| Savoy | ||
| Sweden | ||
| War of the Spanish Succession 1702-15 | France | Austria |
| Spain (Philip of Anjou) | Spain (Habsburgs) | |
| Bavaria (1702-04) | Dutch Republic | |
| Mantua | England + Scotland / Great Britain | |
| Prussia | ||
| Hanover | ||
| Savoy | ||
| Portugal |
as you can see France fought most of these wars alone, or with only a few allies. the geopolitical reasoning--particularly for England--behind these wars of shifting alliances was to maintain a balance of power in Europe. the goal was to prevent any single state from ever achieving hegemony over the rest of the continent. as France was long the largest, wealthiest, and most populous European state it is then not surprising that it found itself the target of a series of alliances aimed at limiting its expansion.
these shifting alliances seeking to maintain a balance of power later came to be popularly referred to as the 'Stately quadrille', beginning with the War of the Spanish Succession and continuing through the rest of the 18th century. this concept, combined with a monarchical opposition to France's revolutionary fervor contributed to the formation of the coalitions against Revolutionary and Napoleonic France.
edit: having trouble with formatting; will work on correcting it shortly. formatting fixed.