That would be confusing!

Like a few verbs, vivre can take a direct object or not. Without an object, it means “live”. With an object, it might be translated “undergo”, “experience”, or “live through”.

When it’s without an object, the years are an adverbial complement of time, or how long he lived. This could be made explicit by using “for” in English or pendant in French.

Compare the adverb:

A) He lived [for] several more years.

Il a vécu [pendant] plusieurs années de plus.

Versus the object:

B) He lived through three years [of war].

Il a vécu trois années [de guerre].

They mean option A in the first example, so the years don’t agree (vécues) as an object would.

In the second example, they mean days he underwent, experienced, lived through. They are the direct object of vivre, so they agree (jours).

Note that nothing in the actual wording of these examples makes us read one way or the other — I’m just working backwards from the agreement they’ve used. But the reasoning could be useful when you’re writing and need to know whether to agree.

[Pendant] les trois jours qu’il a vécu après l’accident il ne voulait pas manger.

My impression is that when the complement of vivre is quantified or numbered in some way, it triggers a reading as a circumstantial argument denoting a length of time. This is the same type of argument seen with verbs of measure such as mesurer and peser, which do not trigger agreement.

However, les jours difficiles does not have any quantifier and is this treated not as a length of time but as a more metaphorical, and thus “normal” object complement, which do similarly trigger agreement with peser (hence “les arguments que j’ai pesés”, as quoted here at the bottom of page 3).

It’s worth noting that very few of the verbs that can show this contrast have the object and circumstantial complement taking such similar forms: usually they are more distinct, hence the confusion.

Certains verbes intransitifs comme courir, coûter, dormir, durer, marcher, mesurer, peser, régner, reposer, valoir, vivre, etc., peuvent être accompagnés d’un complement circonstanciel qui exprime la durée, la distance, le prix, ou la valeur (compléments circonstanciels de mesure).

Dans ces cas, le participe passé reste invariable. Par exemple :

Ce livre m’a coûté cent francs => Les cent francs que ce
livre m’a coûté.

Les années qu’il a vécu pauvre => Les années pendant lesquelles il a
vécu pauvre.

Cependant, courir, coûter, peser, valoir, vivre peuvent être transitifs et admettre un complement d’objet direct (COD). Donc, leur participe passé varie.

En particulier, vivre est transitif lorsqu’il signifie passer, éprouver.

Il n’oublierait pas les moments qu’ils avaient vécus (c-à-d passés) ensemble.

Source: Grammaire: Les Guides Le Robert & Nathan, p. 15-16.

P.S. Il y a une nouvelle édition mais moi je ne possède que la précédente.