A: Interesting question. As far as I know, the flavors in cigar tobaccos cannot be “diluted” or weakened in the usual sense of the word due to high humidity. However, as you noted, the cigars will become more moist, which is why you have a harder time lighting them. You may have also noticed that when you smoke a cigar outside, the aroma tends to take on a more floral character. This may also be why the flavors taste different to you, since the nose has a big effect on how flavors are perceived. But they ought not taste weaker, either.
Additionally, when you relight it could be that not all of the leaves are burning together, so you may not be getting the full effect of all the flavors. Think about when you’ve lit a cigar and only half the foot ignited. The cigar does not taste the same. Come to think of it, if you’re relighting often in humid weather, eventually the flavors will start to taste bitter and stronger.
When you have a moment, just for fun with a cigar you can afford to spare, remove about an inch or so of wrapper leaf and smoke only the filler and binder. You’ll notice an immediate difference in flavor; then see what happens when you reach the remaining wrapper leaf.