How should I troubleshoot Wi-fi timeout issues?
You don't say what OS you are using but I would suggest looking at the LAN to see if there is any WiFi channel or address conflict with your en1 connection (Mac mini airport or NAS?); also check that the AP has a channel that does not conflict with a nearby neighbor and is at least 2 channels away from its nearest competitor (if AP is 6, any neighbors should be 8 or 4). After that, try deleting your connection on the laptop and adding the AP and network info including the DNS. 
You might also check that your LAN AP is the first in line in preferred networks and that there is no other Bluetooth, FireWire, etc. network enabled.