I had the above issue with my New WDTV Live and eventually found the solution which may help some owners I believe this is most likely to apply to Apple OSX users:
WDTV Live latest hardware and software (2013)
OSX Mountain Lion 10.8
TVMobili (streaming Server)
Virgin Super Hub (Router)
The additional issue was once the signal dropped it was impossible to reuse the WDTV without powering down (unplugging) both the super hub and the WDTV as the WDTV could not find the router again Having spent hours adjusting the router channels, trying different videos (all waiting 20 mins each time) and speaking to the ISP / WDTV / helplines I changed the unit (suggested by wdtv) only to find the same issue with the signal dropping, if this was a weak signal why was it so consistent (every 20mins), I was pulling my hair out , I suddenly thought what could be creating the time issue with this.
The solution: go to Preferences/Energy Saver/Computer Sleep which was set to 20 minutes I found this timing approximate (Change it to a longer time) , there are about 4 other options but none effected this after several adjustment tests this was the cause and sorted my issues. I have no idea why this caused the wdtv & super hub to need unplugging before they would work again.
For the record TV mobili proved an excellent streaming server which lets you choose from multiple folders to stream from and so far has helped play every format I have thrown at it, I hope this helps it may even apply to windows users.
Hope this is of use