Strobe firing issue?

I have an AlienBees B800 strobe which is connected to my camera with a sync cord. I'm new to using the strobe light but I have practiced with it at home...figured my way through the "black bar" issue and all that. My issue is that the strobe randomly won't fire. I was doing a newborn shoot today for a friend...I would get everything set up, get my exposure correct and test it out before placing the baby in. Then I'd get the baby posed and bam no strobe firing. It was driving me crazy. Is this an issue of not having settings correct or is this a sync cord issue? Should it be flashing every time regardless of my shutter speed? I feel like ISO 100, shutter speed 1/200 and f4.0 the thing should be flashing in a darkish room.

Its most likely a pc sync cord issue. Thats a pretty unreliable system. Your best option is to pick up some radio triggers.

Sync cords suck. +1 to getting some wireless triggers. Sync cords are great for backup.

I'd agree with the above but with the qualification that cheap, low quality sync cords tend to be less than reliable. Same with any product including wireless triggers. You could try swapping the cord if you have access to another or look at wireless options.

Should I stick with the Paul C Buff trigger system or any other recommendations?

The paul buff cybersync trigvers are great, they just dont fail. That said they are pretty much a one trick pony. Since pretty much any trigger can work with them you might also consider cheaper triggers like the yn603 or if you are intp speedlights the yn622c. I still use my cybersyncs with my bees and love them Buff also offers the cyber commander that works with the + versions of the cybersyncs to give you remote power control.