I feel like they are the type of rich parents who travel the world and never pay attention to their own child.

I honestly think so.

Nope, I don't think they're alive.

I don't think they're alive. If they were then the father would be there teaching his son how to be the new king of the kingdom and put pressure on him to find a bride soon. Most kings do. But no he has that old guy (don't remember his name. lol.) to help him help. It's pretty clear his parents aren't around anymore.

^ Grimsby (love him!!)
I agree that this seems very likely, but then again, it could be possible that they're just frequently absent from their son's life...

i think they died when he was young.

Looks like it.

Most likely they are dead, it's impossible that they wouldn't be there at all if they were alive, like it was mentioned before, they would have tought him how to prepair to be a king and find a wife, etc, but instead Grimsby was doing all that and looking after him, basically being his only family. Also in the second movie there is no way Eric's parents wouldn't be there to see Melody, his and Ariel's daughter. And they were not at Eric/Ariel wedding too.

more likely !

I think they're dead, which also begs the question of why he is still PRINCE Eric.

I don't think they're dead, if they are so Eric's should have be king instead prince(or is his elder brother the king, I don't know)

"King" sound less romantic than "princess", less cute also. "King" isn't as much associated with youth, beauty and goodness as "prince". Same with "princess" and "queen".
We all know Disney loves killing parents. Of course we will never know.