Can I have multiple wireless APs use one ssid/wpa

Just make manual settings on PC for that wireless network.

Set this network as preferred and no more typing and losing connections.

Regards  

It should work and you be able to roam fro ap to ap. Make sure the APs are in the same L2 subnet. The APs should be sharing the exact same SSID and security setting (pre-shared key and encryption). The channel used should be different from each neighboring AP reducing interference.
When connecting to the network you should set the option to remember the network in order to not have to re enter the key.

Specifically the channels used should be at least 5 apart (1, 6  or 2, 7, etc) to avoid interference.

"I set them up that way but when you move from one end of the building to the other you need to enter the key again." For this you need industrial WIFI APs, not the ordinary "home".

You need something like Zyxel NXC-8160, but its quite expensive ($2400)
(http://www.zyxel.com/web/product_family_detail.php?PC1indexflag=20040520161256&CategoryGroupNo=F89D7490-FC19-49EC-AA97-AEBB09B68F79)
..."The unique solution enables the signals on the same channel to be transmitted through every access point in the system without the co-channel interference that plagues other WLAN solutions. Clients only need to associate with the controller once in order to move within the channel blanket without experiencing inter-AP handoffs. As a result, different WLAN security settings will have no impact on its speed; that is, the zero-delay roaming functionalities can retain its outstanding "always-connected" performance even with the most sophisticated encryption and authentication mechanisms applied."

There are many other vendor solutions (Netgear WFS709TP, Cisco ..., etc.)

Take a look on Cisco AP541N-E-K9, it seem to be right thing for you (for aprox. $350), but I dont know what else is needet (APs etc.) to confirm your needs.

thanks for the link with the additional conversation. It was the channel  overlaps that caused my issue.