I have the exact same problem, except my phone isn't rooted. It will connect to wifi networks without issue, but will quickly "hang" on the network after starting a download and I will have to restart before it will work again. This is obviously a software bug because restarting Wifi will return connectivity (for a few seconds) without having to do anything to the networking equipment. All my other devices access the network just fine.
When it isn't working, applications claim that no connection is available, even though 3G is still working. Sometimes the Wifi connection will automatically drop, sometimes not.
I have read that avoiding 802.11n or AES encryption will help, but I don't observe that to be true. Download enough data, and it will hang.
This is truly worrisome because I am effectively locked out of using Wifi at all. Really a huge problem with this Droid X. I'm upset with Motorola.
Interesting to note, they acknowledged the issue with Froyo and claimed to have a fix in the "next version". Now that I'm on GB, it seems to be alive and well, if not worse. Please join me on the Moto support boards asking for a fix. They need many voices to join in before they listen.