How much do you know about your Wireless LAN?
Is your wireless network secured with WEP or WPA?
Is your wireless network setup to support 802.11b devices?
Amigas don't have much bandwidth so your network, wireless or otherwise will pretty much be limited to around 10Mbps. Adding WEP encryption will slow it down some more.
There are also drawbacks to having an 802.11b (11Mbps) device on your router as with most chipsets/firmware the entire wireless (2.4GHz) network slows down to accommodate the older protocol.
What I did is I bought an old 802.11g/b wireless router on eBay and set it to 802.11b mode only. I did not use WEP or any type of security as it is a bit of a hit & miss with Amiga OS 3.x software. I secured it using MAC address access list which will only allow the network devices I enter.
Unfortunately, networking on the Amiga has never been easy, mostly because network technology keeps moving forward and the Amiga doesn't.
But once you set it up you'll never need to deal with it again. At least until the hardware fails.