There can be a few reasons this happens:
1) Sometimes the connection is dropped between the website and the companion app. This seems to happen more frequently depending on the manufacturer of the device and the power settings. For example, some devices will shut off the wifi when the screen turns off and periodically wake it up to perform checks for email. This will prevent the website from successfully transferring the assets/extensions. You can increase the display timeout if this is happening frequently.
2) We've also seen issues where the OS doesn't allow for updating the dex cache in the private data. The assets will transfer, but then you will get one or more runtime errors related to any extensions you are using. You can try clearing the private data for the companion in the Settings > Applications menu.
3) As Taifun mentioned, clearing the /AppInventor folder can remove outdated assets/extensions and free up space on the SD card (emulated or real). If you're running low on space this could also be a potential cause for not receiving assets.
If the error is happening frequently, you can also use your browser's developer tools to monitor the network traffic between the server, your computer, and the Android device. Specifically look for HTTP 500/403 errors as these signal that something has gone wrong.
Evan