Punctuation is a matter of style, and as such you should be guided by your manual of style. Good punctuation leads your reader to make the right parsing choices, and bad punctuation leads your reader down so-called "garden paths", dead ends of wrong parses. Your reader will recover from a wrong parse by re-reading your text, but that's an unnecessary burden. The rules given by most manuals of style allow for the writer's judgment. Let's examine your sentence in light of the foregoing.
To date, only one HIV vaccine trial (RV144)
To date means up to now and is probably best followed by a comma. That's because to date is also an infinitive meaning to see socially or to assign an age:
To date only one sister at a time is probably a wise idea.
To date only one rock sample may lead to an erroneous result.
Of course as soon as your readers see "HIV vaccine", they will know that you're not giving social advice or talking about radiometric dating, but the comma makes sure they're not distracted by the possibility. Now let's examine the second half:
elicited a protective immune response, and in this trial protection was weak and short-lived
English allows adjunct nouns to act as modifiers, so trial protection might mean something judicial:
In the US, the 6th Amendment's trial protection is an important right.
Or it might mean something being attempted, along the lines of a trial separation. The cure is to place a comma after the introductory prepositional phrase "in this trial".
The question of the comma after response is trickier. Here you have a compound predicate "elicited ... and was". As a general rule, a comma only separates a conjoined clause (e.g., "trial elicited, ... and it was"). Unfortunately, the and could also signal a compound object:
elicited a protective immune response and a concomitant increase in T-cells.
Alas, punctuation can take you only so far, and the over-burdened comma cannot prevent both possibilities for misunderstanding. This is where you rephrase:
elicited a protective immune response, which in this trial protection, was weak and short-lived.
This changes the syntax without changing the meaning. The comma now signals a non-restrictive relative clause modifying immune response.