The short version:
Tellius cosmology revolves around order, and the loss of power in laguz/beorc relationships that result in children isn't a punishment or a weird quirk of genes - it's an enforced balance between the parents.
The long version:
Part Four of Radiant Dawn pushes the popular "order vs. chaos" conflict that crops up in dozens of RPGs everywhere. (Suikoden comes to mind.) Although Ashera is depicted as evil and/or crazy, and definitely in the wrong, Yune's stories about when she was Ashunera, and the revelation that Ashera and Yune together equal that primordial goddess, say to me that Ashunera is a goddess of balance - or at least one of the natural order, which possesses elements of both. A world that's all chaos or all order would be unlivable.
The herons as creatures of perfect balance also somewhat underlines this theory, in my opinion. They don't need to fear Ashera's judgment or Yune's chaotic influence.
Now-- this is a matter of personal experience and observation, so I can't say it's universal, but: both parents need to be on somewhat equal footing. It's difficult to marry two vastly different family backgrounds (class issues, for instance) or educational accomplishments (Ph.D vs. no academic training). Not impossible, but hard. These basic differences can lead to huge gaps in communication styles, for example.
If you consider the difference in physical capability between a laguz and a beorc, it's glaringly obvious. Unless we're talking about a heron, the laguz will always be stronger, and of course they have the ability to transform, and much longer lifespans. It's a situation that's ripe for contempt (for weakness, for animal characteristics), angst (one will die long before the other - it's almost suicidal to stay and watch them get old and die), there's public prejudice, and if you believe Nasir in PoR, laguz customs are vastly different from beorc customs. I'm thinking this has a lot to do with eating habits actually, but I think they actually say laguz have a stronger grasp on their instincts, and that can lead to drastically different ways of thinking.
Judging by what we see in the games, the laguz who've lost their power maintain some of their old characteristics (Lehran still has his wings and Almedha is still crazy possessive), but they lose the ability to transform, and any other special abilities that come with their race, like galdrar. Lehran can still sing, which you see during the extended ending if he survives, but the magic is gone and he can't make anything happen with his voice. We don't see enough to know if he still possesses other abilities, like sharpened sight or hearing, or whatever instincts are natural to herons. But generally speaking, the playing ground was leveled between these two and the humans they decided to marry. Even though I imagine Altina could have picked Lehran up and thrown him over a wall, his heron abilities set him apart. Though Almedha doesn't seem the type, she could have leveled Nevassa by herself before she had Soren, and that's a rather steep, unfair power imbalance.
So, my theory is that the loss of power is a natural balance between parents. We're talking about a world in which people transform into huge cats, so I don't think it's out of the question. The idea occurred to me when I was reading something or other about laguz and beorc being separate evolutions of the Zunanma, and if the gene pool split somewhere back there, why can't it come together again with a superior race melding the two parts back together again - in the Branded?