The reports I read show that Abbas and Olmert were several weeks away from a deal. The Palestinians never ended talks. They did not know that their deadline was so short, they could not have known. They wanted to negotiate on smaller finer points, and it would have been irresponsible for them to not do that given the importance of the details of the deal to their people. The negotiations ended because Olmert got taken down by a domestic corruption scandal. Once the explosive details of the scandal were released, Olmert was in no position to sign a deal politically.

The negotiations ended because Abbas flew off to Amman with his negotiators for no reason, cancelling a meeting to work on finalizing a map. Olmert resigned the next day, realizing he had nothing left to work for. Even so, Abbas could have continued, scandal or not: Olmert may not have been able to sign a deal himself, but the Knesset could have approved it regardless. Or used it as a framework for a future deal. Abbas did neither of those, and only weeks later said "Olmert couldn't have continued negotiating". Then a few years later he said the Olmert negotiations would have succeeded.

Shame he left them, then.

Arafat and Barak is a different situation since Arafat rejected the deal, unlike in the Olmert negotiations. Arafat thought that the provisions for refugees and for east jerusalem were unreasonable (Barak's deal did very little on both fronts). Regardless, Arafat is dead and Abbas is in power so his negotiations are the relevant ones.

It's not irrelevant that the Palestinians have time and again "missed an opportunity". Especially as to why: Arafat's negotiator Saeb Erekat said they needed 6 more weeks to draft a deal. Convenient, then, that Arafat did a little world tour (as noted by Clinton) before starting talks at Taba or accepting the Clinton Parameters.