Running Breakaway 24 / 7 ?

When the current version of BBP was released, the specs were for a server grade machine, at the time this would have been an expensive beast to build but these days, an entry-level PC will pretty much outperform anything you could have built in those days.
The specified O/S is Windows XP and for good reason, Windows XP works rock solid when all configured correctly, in my experience, anything after XP is a headache.
You will need a good high quality 192Khz output samplerate soundcard. The list of choices used to be mind-boggling but since the shift in PC architecture to PCI-e the choice has reduced but it's not quite so simple. There were a load of great soundcards in PCI format, many of them have since been discontinued but a few were migrated to PCI-e. Examples would include ESI Juli@ XTe and EMU 0404 PCI-e.
The ultimate soundcard for BBP was always the Marian Trace Alpha but this is only a PCI card (although PC mainboards can still be obtained with PCI ports) but seemingly the new equivalent is called a Marian Seraph AD2.
There are also a few USB or Firewire interfaces suitable.
At the end of the day, the soundcard choice is the most important part as this is ultimately what delivers the MPX output to your FM transmitter.
I have a station which has been running for seven years on the same (XP SP3) machine. With the nature of PCs, they do require occasional shutdowns, maintenance and CMOS battery replacements but I have known it to run for over a year without interruption.

If you're wondering if you can put a computer on a mountaintop, with Breakaway as your main processor and expect 24/7 reliability, the answer is Yes.

I've had a couple of stations on BBP since early 2012.  The computers are common Dell Optiplex models, with SSDs and UPS backups on them. Since installation, they haven't been touched, other than (roughly) annual checks to make sure CPU and cabinet fans are OK.

I also use the software at my drive-in theatre.  Those computers don't run as long as the radio stations do, as we're seasonal out here.  Still, they run for roughly 7 months at a time, before being shut down for the Winter.

I think the trick is to dedicate the computer to the processor… everything you don't need should be removed.  Mine have had VNC on them, and eventually Team Viewer.  Otherwise, BBP is all they do.