In short, I'd leave it running 24/7 if you have use for that kind of run time. One rule of thought here is if you are powering the box up more than four times in a day I'd leave it running for the day and only shutting it down when it'll see the most consecutive hrs powered down. If you find yourself wanting to schedule recordings throughout the day and night, then I'd let it run for 24/7.
I've been into computers for well over 20yrs now. Over the last 15 I run my computers 24/7 and have never had a hardware failure due to MTBF in the first 3years. That seems a bit shy of what we'd like them to last and that is worst case scenario for me. I still have my old 486-66 that was my prime box for 3yrs. It was replaced by my still functioning P166 again that lasted 3-4yrs in prime use. My current computer has been going for 2yrs with a few upgrades here and there. The old hardware that?s been replaced by upgrades are running in my wife?s box, or the PVR or are sitting on the sidelines waiting to be used in another box later. The biggest issue I've always had to deal with was dust over time. I've added scrub pads as filters to all my intake fans and that problem has been solved. Now the only issue I have is power consumption for three computers that run 24/7 at the house. The use I get out of them qualifies running them 24/7. My main box I use as an FTP server, gamming, post-processing of videos, and other batch processes that'll run in the deep nights or when I?m work, all justify it going 24/7. My wife?s computer, well it?s so slow its helps with the WAF just leaving it on. The last box is my PVR and with how I have SageTV setup, it pretty much records 24/7. It also does automated maintenance on drive cleanup/defrag, commercial detection and some other processes I'll farm off to it when I don't want to tie up my main computer. Since it also drives the bedroom TV's via mediaMVP's, its needed running, not powered down. But enough about my setup..
Things like system noise, cooling, over all power consumption, constant on and off are things to consider when thinking about going 24/7 or not. MTBF is a funny thing, you can ask yourself, "did they consider power cycle on a daily basis or not?" When you power up, things get hot, really hot. They may be running well within spec on the heat, but components do expand when they heat up to run. Power down and they'll cool off and shrink slightly. Do this enough and you'll have a failure sooner or later just due to this aspect alone. I'd venture to guess that the real key here is power consumption over all will be the biggest issue. Having a box idle for a majority of the 24hrs is not good use of that power. Machines today, even the tiny ones do consume lots of power, esp. if that is a gamming box with a honker power supply and video card. If you really want to dig into this, I think you can find some calculators on the net that'll help you figure out what your PC's power consumption use is, and your monthly cost on running it. Personally I've never looked mine up, but I am willing to pay for the use I get out of 24/7 operation for three computers.
Hope this helps,