I found these two threads which mention similar behavior but didn't find a solid resolution to the problem:
Unwanted shutdown Linkstation Live
Linkstation Live HS-DH500GL Beeping
I updated my Linkstation last week after discovering that firmware 2.21 had been released. I had been using the firmware released last year in January to address the PS3 compatibility (version 2.11 I believe) until then, and I never encountered this problem before updating to 2.21. Since updating, I've encountered this problem only a few times and always randomly.
The reason I'm posting here is because my experience with this problem seems to be a bit different than the two I referenced. My Linkstation has been in an area with decent air flow, and hasn't changed locations since I've owned it (nearly 2 years). While it's on a desk, it's within a few feet of a window that I've had open all weekend, and yet the problem has occurred both in the middle of the day when it's been warm and humid, as well as in the middle of the night when it was cold and less humid. The fan seems to be working properly, and I even opened it up and blew dust out of it and any airflow channels with a can of compressed air. The device is connected to a UPS that has line conditioning circuitry, so I don't believe that it's happening due to a brown out or minor surge.
Naturally since the device is powering down, I can't access the web interface to find out what the beeping is indicating, and even if I had it configured to email problem reports, my ISP (Comcast :() requires a more complicated means of sending email through their servers than the Linkstation configuration allows. The beeping is a constant, regular beeping without any pattern beyond being equally spaced. It doesn't stop or break until I press the power button once. I can then turn the Linkstation back on and use in normally for hours, but the problem always seems to occur when I'm either out of the room or asleep, but it hasn't occurred frequently: only 3-4 times since Wednesday of last week.
Any ideas?