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The answer is NO, this is not normal STB behavior.
The only times that I am aware of an STB turning itself off under normal behavior is when you leave it tuned to a channel that you are not subscribed to for an extended period of time, or if you have it connected to a TV through an HDMI cable and the box senses that the TV is turned off. (In the latter case, check to make sure that your HDMI cable is securely inserted on both ends. Or swap it with a known good cable.)
If the STB is just turning off (standby mode) and the TV and other equipment are remaining on, this is very unusual. My first thought would be to make sure that no one is touching the remote and that the remote is not pointed at the TV when this occurs. This would eliminate the possibilities that someone is accidentally pressing the power button, or that a faulty remote control is turning the box off all by itself.
More common is the complaint that the box resets frequently (also not normal STB behavior). When this occurs, you'll hear a click, the front panel (if you have one) of the STB will momentarily go blank, when the box comes back on it will be in standby mode, and when you press the power button a red startup screen will display.
The most common reasons that an STB resets are as follows:
I have also found that performing certain activities can increase the likelihood of a box reset. These activities include prolonged Guide and On Demand menu use, especially looking up a lot of Information page descriptions. If you are performing the same type of activity each time the STB resets (e.g., looking up the same information page to the same program), this is a rare and unfixed issue that I've already notified Verizon about.
The bottom line is, if you're not having power issues and your STB has enough clearance around it to stay cool, you're probably looking at a bad box. You'll need to contact Verizon directly and have them walk you through all the steps to exchange your STB.
Short of that, you can always try an STB Auto Correct. Post back here if you need help doing this.