One of the most vexing problems in historiography is dating an event when the usual sources offer conflicting chronologies of the event.
Statements
One of historians' biggest problems is when their usual sources have conflicting ideas about when some event occurred.
They should try to have fewer trusted sources, so that there's less likely to be a date mismatch among their group of sources (maybe eliminate the less credible sources from consideration).
Once they winnow it down to just a few sources, the problem still occurs. They still often have conflicting dates.
When this occurs, they may try on their own to figure out what the correct date is, but sometimes they're unsuccessful.
Evaluate
This stimulus definitely doesn't seem to have obvious Conditional / Causal / Pivot markers.
The last sentence is vaguely Conditional / Quantified: There's something vaguely Conditional/Quantitative about the once this is achieved, as often happens, though on occasion.
The gist of the paragraph is that when historians are trying to figure out the date of event X, they check their usual sources. When they get conflicting answers, they don't know what's right!
The author advises them to prune away some of their sources, thinking that if you ask too many people the same question, you're gonna always get different answers.
When historians get down to their few, core sources and they still get different answers for the date of event X, then they try to figure out which date is right on their own (sometimes unsuccessfully).
Goal
If I had to predict, I would feel like that "though on occasion unsuccessfully" is too weird to be in that sentence if they weren't going to use it for something.
So let's look for the most provable claim, but it might address that idea that .