I hate to say it, but the client device itself is responsible for determining which AP to connect to. It runs its own internal algorithms based on the radio environment, so there's little that can be done to convince it to leave a particular AP alone.
One thing that might help is to disable the 1 and 2Mbps data rates. This drastically reduces the poor-quality range of the APs. If it's connecting at that poor of a signal, this might take care of the problem.
If you're desperate, you can always block this client from using the far-away AP. The downside is that the client might legitimately want to roam to this AP one day, and it won't be able to. If you want to use it as a temporary fix, use this config on the AP:
conf t
access-list 700 deny xxxx.xxxx.xxxx 0000.0000.0000
access-list 700 permit 0000.0000.0000 ffff.ffff.ffff
dot11 association mac-list 700
where xxxx.xxxx.xxxx is your LinkSys adapter MAC address.
I hope that helps!
Jeff