1. You lost it
Well, shmucks, it rained and you lost your sugar crystals. Guess you'll have to replenish your sweet reserve. As sad as it may seem, plenty of animals do this with their fat stores, so your dilithoids can definitely survive this. Heck, maybe this helps the dilithoid. Think about it; they get that sugar from sugar cane, but why not from other dilithoid? Dead dilithoids or puddles of dissolved sugar left by your less fortunate brethren are like sweet gold!
And, remember, there's a chance that the desert sand will absorb the water but not your sugar, leaving sugar deposits you can eat to recoup your losses. Or if something else gets your sugar, maybe you can eat that something.
2. You never lost it
Gelatin, the main ingredient of jelly, is made mostly of collagen. This protein is common amongst Earth organisms, so what if your creatures store their sugar in masses of jelly instead of crystals? Additionally, non-dissolving sugar is a thing; just add a fat coating and voila! Your sugar is safe! Granted, this will likely result in a lumpy creature, as this would lead to your sugar crystals being stowed beneath a layer of blubber.
In nature, you adapt or you die, and these Dilithoids will be no exception. Either they avoid losing their external sugar to rain by avoiding rain, or they store their crystal securely inside themselves. (Or, perhaps they simply form non-soluble crystals?)
3. The circle of life
Finally, perhaps the Dilithoids sense the rain coming and take shelter, or perhaps the Dilithoids go lemming-style, more or less. Before the rain comes, they mate and lay eggs, hide the eggs where the water won't get to them, and then they wait. The predators come, they eat the Dilithoids, and none of them struggle. Why? Because the flood is coming.
Each foolish predator who came to eat them has brought upon themselves their own doom, ensuring they'll drown in the flood and their sugar-saturated bodies will become food for the baby Dilithoids. Every candy-loving predator is storing sugar in their body, massing it, and once they die, that sugar-and everything else composing their carcass-will feed the next generation of Dilithoids.
Because of this, and their gift for repopulation, Dilithoids don't often resist predation, as the predator's success will become their own. Sooner or later, the sugar will return to their kind.