Not one but two good carpenters have told us, "Wooden posts should not be set in concrete but in gravel. If you set them in concrete even pressure treated lumber will rot at the top of the concrete, affected by the water that pools there."
So, why did we let this very nice trellis be set into concrete? Not even 6 years later both posts seem to have broken loose. As predicted, at the top of the concrete.
We've braced them for now since replacing them requires digging better done in finer weather -- to move all those nicely established plants out of the way, extract the old supports and put in new posts!
What's Up 168: Water a pot, seed for mildewed lawn