if the little red light stays on dim the becm isnt sleeping
i suspect someone has disconected the aerial to the rf receiver (common bodge) to get round it and thats why you need to be so close to pop the doors
you need to get the becm to sleep and to rule out the reciever disconect the power plug to it once youve locked the doors (with you in the car) then wait exactly 2 minutes and the little red light should go out
the reciever is on the drivers side under the lump of plastic the rear parcel shelf sits on, fold the seat forward and undo the crosshead screw then prize out the plastic rivits along the side in the boot, then it sort of pulls off (there are a couple of clips holding it against the rear glass but they should just pull out)
the reciver is a little black box about the size of a fag packet with 2 plugs, the purple cable is the aerial and the other black plug is the power to it