[bartkappenburg]

Wouldn't help: the latency to the relay box is at least as good as having the physical key nearby.

[icebraining]

That can't be true, because the request/reply still has to travel all the way to the key and back.

[gambiting]

If the receiver is accurate enough(we're talking nanosecond precision) then you can absolutely tell if the key is 1m or 10m away, so a relay wouldn't help at all.