How do persistent items work in Battlefield 4?

Solution 1:

I did some testing by myself in the Testing Range on Xbox 360, killing myself via grenades or various hilarious helicopter mishaps and then seeing what persisted after respawn. Here's what I learned:

Despawns on death: First Aid Pack, Medic Bag, Ammo Pack, Ammo Box, C4.
These disappear when you die, no matter what loadout you choose next. These may persist until you respawn, I couldn't test that by myself. The C4 is a bit weird; it occasionally lasts a second or two after respawn and if you're fast enough you can even detonate your last spawn's C4. My guess is a timer starts to remove it when you die.

Persists as long as equipped: EOD Bot, MP-APS, Radio Beacon, T_UGS, SOFLAM, MAV, Mortar, AA Mine.
These stay in the world where you placed them after you die, and you can respawn and re-connect to them. If you remove them from your loadout or change kits they disappear.

Persists forever: M15 AT Mine, M2 SLAM, Claymore.
These stay in the world where you placed them even if you spawn with a different kit. Note that there are limits to these items, like only 3 mines of each type. If you drop a 4th mine the 1st despawns.