After the latest update with the objects editor, unlimited ammo no longer works for the campaign editor.
Edit: Only works for some missions, stopped working on mission 5 or 6 and started working at the end of 8.
I also ran into this problem; had thought it was because I forced some weapon swaps with the infinite ammo, but it is not working with start weapons either. Invulnerability is unaffected.
For me the entire editor is “Not Responding” when I click save. 
I don’t want to derail this thread but that is due to Horizon downloading a file from the server. Keep it “unresponsive” and it works fine after a short wait.
Instead of selecting the ‘invincibility+Max Ammo/Grenades’ tab, select the 
on both Weapon One and Two in the ‘Biped Object Values’
Once done something like this should show up.
Type in the amount of Clips and Ammo you want on both weapons.
Note: Keep the amount under the Max amount, do not select “Max Ammo”
Example: Remaining Ammo: 30,000 Ammo in Clip: 30,000.
You can also do this with Shields and Health and your Grenade count.
Note: Remember to keep everything under the Max amount.
https://www.wemod.com/forum/125-horizon-tutorials/131270-horizon-|-how-mod-your-halo-4-campaign.html
For me the entire editor is “Not Responding” when I click save.
Just wait a couple of seconds, and you should be fine 
.
You shouldn’t need to manually navigate to the weapon and set it’s ammo like Hero said, the “Invincibility+Max Ammo” button should automatically do that for you.
To clarify, did you start the level, then instantly save and quit?
I just tested this, and the only problem I’ve had, is that, when you make a gamesave at the very start of the level, before any actual check point, sometimes the gamesave is made before the game gives you your weapons.
Example:
I just booted the map “Shutdown”, I saved the game before my first checkpoint. My gamesave said I only had an assault_rifle. But when I booted the save, the game would give me an assault_rifle(a new one), and a LMG. Because of this, using infinite ammo on this save would be useless, because the currently held weapon in the save, wouldn’t be what weapons I’d actually be given when I started it up. In fact, the gamesave in this test was made before the level had even actually begun, (so even half the things in the levels such as marines, weren’t in the gamesave).
If this is the case, the solution is to get to the first real* checkpoint, and not just boot the level then save. And if it was the case, please let me know and I will add it to the “Notes” tab so future users don’t encounter this.
If this isn’t the case, please post more details about your problem, the level name, where you were, and possibly post your save file.