Your cells are too large. The client's job is to stay associated as long as there is a strong signal. If there is a strong signal there is no reason to jump ship. it sounds like you have too much overlap between cells if you are still associated to AP1 when you have moved in range of AP 3.
You seem to now have the un-envious condition of having no load balancing across your infrastructure. One AP will get most of the work load while others go under-utilized.
The way to fix this is to survey your facility for smaller cells. It sounds like you can probably get away with turning the power down on your AP's a bit, but I have no idea what your facility is or what kind of antennas you are using, so piddiling with the settings without benefit of a survey is strictly up to you.
If there is an upshot to this scenario, you obviously have coverage. As long as there are not too many simultaneous users, you should be ok. But know that as your network becomes more and more congested, your problems will increase exponentially.
This is the number one thing that I see when troubleshooting WLAN's, so don't feel like the Lone Ranger.
Things that may help include, turning down the power on the AP's, turn down the power on the clients, only allow the higher data rates unless the specific client you are using requires them (Old Symbol barcode scanners etc..)
The way to absolutely fix this is to perform another survey and design smaller cells in such a fashion that you still have coverage where you need it and the client devices actually associate to the AP's they are in proximity of. This may require more AP's but the payoff is a solid infrastructure with physical load balancing and more aggregate throughput across the network. Decide what your needs are and your future growth plans and use these factors in detrmining how big your cells should be. Keep in mind that the limitations of the building itself and materials used to construct it often make a lot of these decisions for you. The object is to find the happy medium.
