Try turning off ZA and see if that affects the problem. You can also check
the ZA logs to see if it's actively denying a connection in these cases.
Look in Program control as well to see what permissions these programs have.
It might be useful to know what signal strength you have when this occurs,
and whether WEP is being used. If you're not using any security such as WEP,
it's possible someone nearby is sharing your bandwidth and making a
connection difficult. I have set up several wireless networks recently, and
in most cases I was able to see unprotected networks available.
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I am running a Belkin 802.11g Wireless Notebook Network Card on my Compaq
Presario 1277 Notebook running W98SE, ZoneAalarm Pro 4.5.538.000, and
Avast! Version 4.1 Home edition.

About 50% of the time, my card sees the wireless network, the Belkin setup
utility tells me I am connected to the network, but I can IE6, Mozilla, and
Eudora 6.1 can not download from the net.  Conversely, about half the time
I can do downloads.

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