New thought: I am thinking and now testing, that the problem is that the WEP network key is not being remembered although until I have tested this a few times it is hard to tell.

When I go into Properties of the card the network key is empty. Alternatively the ****** markers are much shorter than the actual WEP network key. Although I am aware that maybe what I can see (as a human) isn't what the system sees - so perhaps I might be onto a red herring ... or maybe not.
It is re-connecting mostly, which is what makes me think I might be up the wrong track on this one.

Things I believe are true:
Rebooting the PC will always make it connect
Typing in the network key will always make it connect
When it disconnects if I quickly get it to reconnect it will do so but if I leave it a couple/few hours it won't

Any thoughts on this?