What determines when grenade pickups respawn in ME3 multiplayer?

The grenade spawns are time based, they're just on a different timer than the ammo respawn.
You can quickly see if there are grenades available in a stash as they have their own distinct graphic.

Also, there are different amounts of grenades per stash depending on the map and difficulty. For example, Firebase Ghost has 2 grenades per ammo stash, on bronze you'll get 2 grenades from each for 4 total. On silver and gold, you'll get 1 from each for a total of 2:

Alright as Yx said grenade resupplies are time based. Also keep in mind that each ammo dump has their own seperate supply of grenades. Grenade resupplies are different depending on the difficulty:

• Bronze = 2
• Silver = 1
• Gold = 1 (more time between grenades i noticed)

Ultimately you will find yourself going from one ammo dump to the next to keep your grenades full restocked, specially if your like me and have a capacity of 3 grenades. If someone else grabs the grenades of a particular ammo dump that you are racing towards and he grabs all of them, you will not be able to get grenades from there till the respawn again.