There are two elements to the way that a McLaren Key operates. This is true for most modern keys, albeit other manufacturers have arguably implemented it better...!
When you physically push one of the buttons (to unlock etc.) the battery within the key is used to send a signal to the car. This is quite a powerful signal with some considerable range to it. Usually this works fine.
When you are in the car and push the 'START' button to power the ignition up, the car is sending out a pulse and is actively searching for a key. The key has a circuit in it which is energised by the pulse and responds with an identity check signal. The car and key 'agree' with each other, and the ignition is allowed to start up.
Since the energy used in the lock/unlock signal is very high, this usually works just fine and unlocks the car, even with a relatively low keyfob battery. The real issue comes from the Transponder feature when people are desperately bashing the 'START' button and being told the key cannot be found.
There are a number of reasons for this. Firstly the detection loops that are supposed to find the key are specifically tuned to ONLY find a key that's within the car. The idea being this minimises the risk of theft, and ensures that you've not left your key on the desk in your garage when you set off or something.
The downside is, the loops are quite weak. Additionally I've personally found them to be VERY susceptible to RF and electromagnetic interference. It seems to me they are not very adequately attenuated, and despite only being intended to listen to one frequency (that of the keyfob) they pick up literally anything else that it's transmitting loudly in the area.
So whilst a solid high power battery in your fob is good to have, it's actually largely irrelevant if the issue you are facing is an external source of interference.
The best place for a key is generally considered to be near (below) the IRIS, or in the seat pocket at the front of the drivers' seat (if you are lucky enough to have the pocket).
Sometimes however, you can also get the opposite issue, it can see a key despite one not being present. Gotta love McLaren...