You're using UnitPickedUpTrigger?

Yes

So the reason this happens is that those items (armor, health, etc) are marked as non-netsynced. This was done as a preliminary measure to avoid too much memory usage due to these items being dropped clientside as loot, for example. Weapon items typically aren't spread around the level so much, so those are properly marked as netsynced.

As a workaround, you can copy the original item and mark them as netsynced yourself. Take a look at this page[ssbd.a000ff.com] on how to extract game assets. After modifying the file, you simply add it as a separate unit to your scenario (eg. "items/armor_large_netsync.unit") and use that as the item.

Also, as an addendum, if you look at the unit file you might see something like this at the top:
The line you want to change is inside of that inc file, so remove that %include and replace it with all the contents of the respawn_armor.inc file. This starts with:
You would have to change this to simply:

Good luck!

Thank you!