This has been an ongoing debate, for all electronics, since the beginning of Robot Time.
Negatives about keeping it on all the time:
1. Any transients, power outages, spikes, thunderstorms, etc. on your line have the potential to stress the electronics and do damage. Even with a surge protector, there's always the chance with a big thunderstorm that your electronics will be zapped. A smaller chance, but still a chance. Ultimate solution: unplug during periods of power instability. 
2. Your circuits have the potential to "age" more rapidly, primarily due to heat. Not an issue with Virus.
3. Your LCD dims over time with use; over a very long time, however, and probably in a way neither you nor your grandchildren will really notice. I still have my '97 Roland XP-80 and the yellow-green display still reads fine.
4. For anything software-based, something in your software system/on your computer might scramble while you're not looking (Norton Anti-Virus might wipe your whole system due to a bad update, say..... just half-kidding! but there it is) some night, and you'll wake up the next day, go to your Virus and start complaining on forums about how the Virus Control software doesn't work.
Negatives about turning it on and off:
1. You introduce transients and stress to the electronic circuits every time you turn things on and off. Negligible, but there. Circuits are happier in a steady state, without power or thermal gradients. Most electronics have the highest probability of failing upon being turned on, due to the initial transients. Again, a very rare issue, increasingly, these days, especially for systems without moving parts (your computer, for instance, is at highest risk with its hard drive for this reason, since it's electro-mechanical, not just purely electronic).
2. You have to wait until it's powered up after you've turned it on.
3. You don't have all those glowing, flashy lights in the dark if you turn it off. 
4. Any capacitors in your electronics will be happier if they get continuous power. This matters a lot more for older electronics than recently-acquired (this moves into "how to maintain vintage synths" territory).
5. For anything software-based, you might have forgotten to save some configuration somewhere and lose all your work or enough of some part of it to completely mess you up in mysterious ways, and will have to start over again, and will show up on forums complaining about how Virus Control software doesn't work.