Since my dad plays my old Diamond version... I'd say, at least in my Pt version, that my dad is a trainer, that he is somewhere out there, probably with a ridiculously strong team and a picture of us three and sending back money he earned in trainer battles or by selling stuff his Pickup Pokemon found. Since I rarely visited my mom back at home since I started my journey, maybe he has since returned for a few days. Hugged my mom. Got a new photo. Since I'm on TV sometimes and it's reasonable that it's big news if a champion gets beaten, he probably noticed that girl that looks a bit like his wife and has the name of his daughter that has come so far. Then he returns, my mom tells him "Yes your daugther got so far, now what did you accomplish?" and hands him a new photo. Maybe he doesn't actively look for me because he thinks I'm busy, and or really angry at him for rarely being there. Maybe we will meet in battle, one day and I will pull out the photo I carry around with me and he will say "We're both trainers, we need nothing else", or maybe that fighting's first. Maybe he will deny being my father, maybe he will tell me he's proud of me, maybe he'll apologize for being such a bad father. Maybe I will beat him, maybe he will beat the tar out of me.
Maybe we won't. Maybe, one day, a coffin will be transported to the local cemetary, or there will be a black-lined letter that said he died in some faraway place. Maybe not.
And maybe, he will return for good one day.
So many maybes! D: Oooops.
As for BW... I'm not past the E4 yet (focusing on my Platinum Pokedex instead xD"), so idk.
As for SoulSilver... I like to think that he's some kind of engineer, one that helped building the wind turbines. Since no one seems to change location even at night, he's constantly working. Working and tinkering. And that my little gadget there broke because he kept tinkering with it. But that he comes home on weekends and stuff. And that he's proud of his little boy that did so many things.