If you shoot an arrow in survival, it is lost from the inventory, but can be picked up and added back. In creative, shooting a regular arrow will not take from the inventory, nor will it add to it upon pickup. Shooting tipped arrows in creative mode will not delete them from the inventory. However, they will ADD to the inventory.

Best method to reproduce:
1. Shoot any arrow in survival mode.
2. Pick it up.
This is what is supposed to happen and does happen: 1 removes, 2 adds it back.
3. Shoot a regular arrow in creative mode.
4. Pick it up.
This is what is supposed to happen and does happen: 3 does not remove, 4 does not add it back.
5. Shoot a tipped arrow in creative mode.
6. Pick it up.
This is what is supposed to happen: 5 does not remove, 6 DOES NOT add it back.
This is what happens: 5 does not remove, 6 DOES add it back.

This is due to a tag called 'pickup':
When set to 0, it means a skeleton shot it and it cannot be picked up.
When set to 1, it means a survival person shot it (applies to creative mode tipped shots, but it should not), can be picked up, and doing so adds to the inventory.
When set to 2, it means a creative person shot it (does not apply to creative mode tipped shots, but it should), can be picked up in creative, but does not add to the inventory.