Reschke,
It sounds like interference from other nearby wireless access points (APs) transmitting on the same channel, since you said you could detect two or three other nearby APs.
By default, most wireless routers and access points are configured to use channel 1, channel 6, or channel 11.
These are respectively the First, Middle, and Last channels of the U.S. 2.4Ghz 802.11B/G Band allocation.
Most folks don't bother to change the channel after purchase and installation, so those three channels are the most used, and most likely to experience interference.
The default Windows wireless network services will attempt to connect to any APs that it can detect, so when the signal from another nearby AP is detected, it will drop the current connection, and attempt to connect to the new one(s).
There are a couple of things you can do:
1. Change your Router/AP to another channel. Try channels 7 through 10 as these are the least likely to be used by others. Don't forget to change to the same channel on all of your WLAN NICs (Wireless LAN Network Interface Cards) in your Laptop or Desktop computers as well.
2. Don't use the default Windows wireless network services. Install the software that came with your wireless network hardware if possible, and setup a network profile specific to your local network. If that is not possible, then be sure to set your local network as the only "Preferred Network", and do not allow your hardware to connect to other networks.
3. Change the default SSID of your network to something else. By default many Linksys routers have a default SSID of "Linksys". If a bunch of linksys routers or APs are all operating within range of each other, and all of them are broadcasting the same default SSID, you can see how the equipment can get confused.
4. Try to pick a SSID specific to you, but not something obvious or common. Don't use your Name, Address, or anything else that would make it easy for a hacker to find or access your network.
5. Setup your network to use WEP encryption, or even better, to use WPA encryption.
6. Once all your computers have working profiles and reliable wireless connections, set your router or AP to stop broadcasting it's SSID. This will make it more difficult for hackers to find your system. If you need to add any additional computers to your network, you may need to temporarily turn SSID broadcasting back on until the new computer finds and connects to the network and saves a profile. Remember to turn it off again.
Good Luck!
CptA