If you ask me, I wouldn't say the problem was poor mortar. You can see big hunks of mortar that have fallen out from between the bricks on the decorative stones. So, that mortar is still strong...and that tells me that it was mixed properly with enough cement in it.

...it's just that it never bonded to the surface of the bricks properly. You can see that because of the fact that the loose bricks don't have old mortar sticking to their ENDS.

When you lay bricks, you spread a bed of mortar on top of the row of bricks you just laid, and butter the END of a brick. You then press that brick down into the mortar bed and push it up against the last brick laid. If you do that with the same amount of mortar on the end of the brick, with the same amount of mortar in the bed under the brick and with the same amount of force every time, you end up with a nice STRAIGHT row of bricks with uniformly wide mortar joints all around each brick. And, achieving that uniformity takes a lot of practice. Without years of practice, amateur bricklaying tends to look like a mouthful of crooked teeth.

Now, if it was only the mortar bed the bricks were being laid into that was too dry so that the mortar never wet the bricks, then that wouldn't explain the ENDS of the bricks being so clean. That's because the mortar that's being used to butter the ends of the bricks is continuously being mixed by the trowel, so it would never have time to skin over. The mortar at the ends of the bricks would always be fresh enough to stick to the brick well.

The fact that the ends of the loose bricks are clean suggests to me that the bricks were wet when they were laid. If the brick is wet, then the surface porosity of the brick will be full of water so that when you butter the end of the brick, the moisture from the mortar won't be absorbed into the brick they way it would into a dry brick. Instead, you'll have a thin film of water form between the brick and the mortar. The mortar then cures, but doesn't actually bond to the brick. When that water film evaporates, you have a very very thin air gap between the brick and the mortar, and when water gets into that gap and freezes, it breaks the brickwork apart.

You can see big hunks of brick mortar that have fallen out of the wall onto the decorative stone. If the mortar wasn't mixed properly, or had too much lime or sand in it, it would be deteriorated. But it isn't deteriorated; it looks pretty solid; it's just not sticking to the brick.

My bet would be on the bricks being wet when they were laid. Perhaps they were rained on the day before they were laid, and never had a chance to dry out. And, that explanation also explains why the damaged area are spotty. When it rains on a pallate of bricks, it's only the top most bricks that get wet.

If it wuz me, I would remove all the loose bricks and buy a 3/8" thick construction grade spruce plywood handipanel of about 1 foot by 4 feet. I say construction grade spruce plywood because it won't be sanded, and that means it'll be exactly 3/8 inch thick, and not 5/16. Cut that plywood into tapered pieces so that they can be pulled out of the brickwork. Set each of your bricks on two tapered pieces of plywood with another tapered piece between the ends of the bricks and their neighbors. Put some weight on that and pack mortar between the bricks. Now pull the tapered pieces of plywood out and let the mortar set up. Then, go back and fill all the holes with more mortar. That's not the way a professional would do it, but you don't have the years of experience it takes to get all the bricks in a straight row with a uniformly thick mortar joints around each brick. The 3/8 inch plywood will give you that; a better looking result, albeit with a lot more work.

Otherwise, remove that brickwork and wooden posts and just put in longer pressure treated wooden posts.