I don't think it holds them while you call in or more precisely blocks them to you on the internet. If it did that I would think the bA agent would not be able to see them either.
I think the phone system is not that bad, just over the last week or so with the US weather problems things snarled up.
I would suggest if you see the seats just grab the phone immediately and certainly leave the page open so you have the details etc but it is not a clever holding system at play.
What dates/route anyway?