I'm pretty sure 3 is the maximum you can have on the field at a time. If you respawn ( or get new one with ammo crates, support can refill rocket/mines with crate too but not with pouch ), putting a 4th mine will make the first one disapear and so on.
AT and AP limit is separate, so you can have 3 of each on the field at the same time.
Lovely, thanks.