It depends if you want to use the passé composé or the imparfait

Verbe avoir – Passé composé
j’ai eu
tu as eu
il a eu
nous avons eu
vous avez eu
ils ont eu

For further details I would suggest you to read this link.

“avait” is imparfait, and implies that the action is over, by two means:

• the action is over (narration is in present tense)
• the narration is in past tense, and the action is ongoing in the time you’re describing, but over now.

Here I assume it’s present tense. If you say:

Il avait toujours un sens aigu des limites du savoir humain.

it means that the action is over, so now, the “acute sense” is gone.