Or get another router... and if the situation doesn't improve, return it.
I'm listening to the AE right now, like you, configured to "join" my existing network and it works great. You can't beat the convenience.
I've used a D-link, Linksys (WRT54G.. cheap), and another Airport Express. The D-Link gave me no problems, but I was living in a house/low density neighborhood. Another Airport Express as the router was the worst sound. Makes sense I suppose, a lot packed in a small package.
I didn't expect there to be a difference in sound vs the linksys but there seems to be. I was having minor drop-out problems with the Linksys in my new place (apartment/lot of singles) during certain hours. Not nearly as bad as my other place during Christmas as mentioned, but for some reason around dinner time and 2 AM, it would drop out for a few seconds.
The Airport Express as router never experienced drop outs for the 2 weeks I had it in.
However, I'm going to stick with what I think is the better sound. As a matter of fact, while writing this, I just switched back to the Linksys, and am quite happy. The 2nd AE as a router and it's sound was starting to tick me off.
If the dropouts become too problematic I'm going to change channels or do some research and get another router.
At our big box electronic store, there is a 90 day return policy....
Or you could always get a really long USB cable as suggested, provided your DAC accepts USB. As for digital cables though, note that the AE and MacMini's optical output is a "mini-toslink".
I'm using a meter long VanDenHul Optocoupler II, mini-toslink on one end, standard toslink on the other (no adapters necessary) into a Monarchy M24.
Not sure if an adapter would degrade the signal/sound, and I'd imagine an extra long glass toslink cable wouldn't be too cheap.
I wouldn't give up on the wireless set-up just yet....this is of course, provided you haven't already tried different routers. Like the other poster suggested, it may very be your neighbors, in which case you're going to have to explore other options.
Good luck.