RAW - Only once when the wall first appears
When the wall appears, each creature within its area must make a Strength saving throw. A creature takes 3d8 bludgeoning damage on a failed save, or half as much damage on a successful one.
The spell does not describe any kind of effect that continues. Only when the wall appears does it say that damage is taken.
If the spell was intended to have continuing damage it would have said so explicitly as it does in other similar spells.
Example of continuous damage language
For example, wall of fire says:
When the wall appears, each creature within its area must make a Dexterity saving throw. On a failed save, a creature takes 5d8 fire damage, or half as much damage on a successful save.
but then specifies the part about continuing damage:
...deals 5d8 fire damage to each creature that ends its turn within 10 feet of that side or inside the wall. A creature takes the same damage when it enters the wall for the first time on a turn or ends its turn there.
Wind Wall has other effects besides damage
The continuing presence of the wall, while not causing damage, does continue to benefit the caster in several ways:
The strong wind keeps fog, smoke, and other gases at bay.
Small or smaller flying creatures or objects can’t pass through the
Loose, lightweight materials brought into the wall fly upward. Arrows,
bolts, and other ordinary projectiles launched at targets behind the
wall are deflected upward and automatically miss. (Boulders hurled by
giants or siege engines, and similar projectiles, are unaffected.)
Creatures in gaseous form can’t pass through it.
Spells' effects sometimes do not mesh perfectly with their flavor
Despite the designers' best efforts sometimes the mechanics of spells do not make sense or do not seem to. In these cases you have three options:
- Ignore the fact that is doesn't make sense and just continue with the spell as written
- Come up with a way to explain the possibly confusing spell effect in-fiction
- Change the spell so it makes sense
Your group seems to have opted for 3, but do be careful when taking this option because it will change the balance of the spell and game depending on the changes made.
But, if 1 and 2 don't make the group happy and the DM is happy with making changes then go ahead. The rules are made to serve the people at the table and create fun not the other way around.
Flavoring the spell to make sense
The fact that damage is caused when the wind is first summoned but not anytime after is unequivocally true (per the above). The issue you seem to be having is making it make sense in game.
One of the more obvious ways I could justify this in-fiction is that when the wall is cast it is very briefly powerful then dies down a bit.
Another explanation might be that when the wall is created is bursts forth in a very strong gust spraying up debris (rocks or whatever is lying around) and spraying those in the area with that. After that, the area generally clear of debris and thus no more damage is taken.
These are simply examples (eg you may not have debris on the ground), but there are many ways to justify it.