I don't get this argument at all. It seems obvious that most of the time an organism gains a property it immediately dies (or fails to pass it to its offspring). They have lots of tries, they're not special.
So: "Common ancestor" my arse. They insist on drawing these diagrams as trees when they are much more complicated graphs.
The question is, do all currently living creatures with neurons trace back to a common ancestor who also had neurons, or are there several neuron-having lineages alive today, each of which traces back to a different earliest-neuron-having ancestor. In the latter case, each of those neuron-having ancestors would have shared a common ancestor, but one that did not have neurons.
The lineage of all life on earth certainly creates a more complicated graph than a tree, but at the time scale needed to create a novel feature like neurons, it certainly looks like a tree. To say otherwise, you'd have to point to a case where genetic information passed laterally between species, rather than vertically from parent to child. This probably has happened [1], but is not so common as to make all tree-shaped charts misleading.
However, it doesn't change the fact that, when viewed from 10,000 feet, the tree of life looks more like a tree than a web. Especially with regards to the question "did neurons evolve twice," very little is lost by ignoring that sometimes cousins marry, and sometimes a virus leaves a chunk of genetic material in its host.