Which player? Maybe I'm just not seeing it, but nothing there looks odd to me.
Can anyone tell me why this player didn't advance?

What's interesting is that the group from which three players advanced, there was a tie for second place so it's as though the rules for only two players advancing were applied across the board when the tournament is clearly set up for three to advance.

Given that the max group size is six, three advance and there were four groups to start (24 players total), if there were no ties in the first round there would have been two groups in round two, not three.
Pure speculation, but could it be that the system tried to compensate for this extra player advancing from the first round so that there would only be one group in the third (and hopefully final) round by advancing only two from those three groups for a total of six players (and that it backfired yet again with another tie, meaning there will be an unintended fourth round to finally decide the tournament)?

That sounds logical, TheGrobe.
echecs06: I am the TD. You can click on "Tournament Home" from the link to find more info on the tournament.

I'd be interested to find if that were actually the case -- is anyone from staff reading that can weigh in?

One of the players (Javad29) I am hosting in a tournament didn't advance to the next round, and I am at a loss as to why not. Can anyone explain this? Here is a link to the round where he was disqualified:
http://www.chess.com/tournaments/pairings.html?id=19939&round=2
Regardless of the original 3 of 6 advance, the rule is maximum 50% of the largest size group can advance from any group. The largest group in round 2 became five. 3 of 5 is 60%. So only 2 plus ties can advance.
In the current round 3 the largest group has four players so in Group #1, 2 (plus ties) of 3 will advance and in Group #2, 2 (plus ties) of 4 will advance.
fyi - For future reference, due to a bug, the largest group in round four will be four players. The maximum size of 6 players you specified is replaced by the largest size of the previous round. If 5 players happen to advance there will be a group of 2 players and a group of 3 players.
One of the players (Javad29) I am hosting in a tournament didn't advance to the next round, and I am at a loss as to why not. Can anyone explain this? Here is a link to the round where he was disqualified:
http://www.chess.com/tournaments/pairings.html?id=19939&round=2