Edit: I should make sure to mention that some studies of great size, either with many many respondents and/or many many data fields could take a very long time to download in this fashion. If downloading manually takes more than a few minutes, you'd probably want to make sure that you're careful about naming your output files so they don't overwrite (i.e. file1.csv, file2.csv, etc). I've helped someone with a study with 30,000+ respondents with 50,000+ data fields, and it took 10 hours to download in the admin module with this type of method, even though the resulting .csv was just 200k or so. In that case, I'd recommend downloading the data inside SSI Web 8.4.6 as Paul Moon suggested, since it will take that 10 hour process down to a handful of minutes.
It is currently not a feature of the SSI Web admin module to have it "push" data from the study to another place. It is, however, simple to automate a "pull". If you have a computer or server that can use some sort of scheduled task, such as the Cron job scheduler, then you simply have to do a web request to the relevant place.
I don't think this is terribly complicated, but I am a web/server developer, so hopefully this really is simple, and not "I do this all day so it seems easy" simple.
Here's a simple example using the linux/unix command-line utility, curl (http://curl.haxx.se/
Basically, just make a POST request to the admin.pl file at the correct URL, and use the following in the POST data body:
Another quick example with wget (https://en.wikipedia.org/wiki/Wget