A shield that has come away from its mounting is usually still doing most of its job, but it is now doing something else as well: moving. Movement turns a heat barrier into a wear item, because the shield and whatever it touches grind against each other.
The first question is whether the shield itself is intact. If the facing is sound and the fixings have simply lost grip, the repair is at the mounting. If the facing is torn or the foil has gone, the shield is finished regardless of the fixings.
Shield fasteners live in the worst place on the car: hot, vibrating and often inaccessible. Captive nuts strip, rivets loosen in thin sheet, and spring clips lose tension after enough heat cycles. A shield that rattles at idle is usually announcing one of these.
Check each fixing by hand where you can reach it, and look for a bright witness mark where a washer has been moving. A fixing that is tight but has a worn seat is already loose in the way that matters, because it will not hold the shield flat against the panel.
A shield is only as good as what it is attached to. The panel behind it runs hot, and thin sheet metal around a fastener will crack from thermal fatigue before the shield fails. That is why a loose shield is sometimes a symptom rather than the problem.
Look at the panel around each fixing for cracks radiating from the hole, and for rust or burn discolouration that suggests heat has been getting past. If the substrate is cracked, a new fastener will simply pull through, and the panel needs repair first.
A shield works by holding a layer of still air, or a reflective gap, between the hot part and what needs protecting. Pressed against the hot surface, heat conducts straight through and the shield becomes a heatsink. Pressed against the protected part, it conducts there instead.
Restore the standoff when refitting, using the original spacers or washers where they exist. An exhaust heatshield that has been tied flat against a pipe is no longer shielding anything.
A loose shield often presents as a rattle that seems to come from the exhaust, the suspension or the boot floor, because the sound travels through the body. Owners spend time under the wrong end of the car looking for it.
Test by tapping the shield lightly with the car cold and listening for the same note. If the rattle appears only when the car is warm, or only at certain speeds, heat expansion or airflow is moving the shield, which points at a fixing rather than at a worn bush. A heat blanket is a different product with a different job, and wrapping one around a loose shield does not put the shield back where it belongs.
With the car cold, push the shield at each corner. Any movement beyond a slight flex means a fixing is not doing its job. Check that nothing touches the shield on either side, and that no wiring or hose is resting on it.
If the shield is intact and the mountings are sound, it can stay. If it is torn, or the panel behind it is cracked, the shield comes off until the mounting is repaired, because a shield that separates at speed does more damage than the heat it was blocking.