Live Tracks gone bad?
How will you be controlling Ableton? Foot controller (SoftStep or Looptimus)? Keyboard?
I've been using loops in live worship for about 4 years now. When I first started, I was using a program called Digital Performer controlled by drum triggers. This method had about a 50% fail rate which needless to say is unacceptable.
Upon switching to Ableton Live about 2 years ago, I have had no problems with the hardware / software. The only issues I've faced have been my fault- using my SoftStep I've triggered the wrong scene or double launched a scene. Sometimes I won't have things routed correctly in a rehearsal but again these are user error and are easily fixed.
Best advice would be to decide on your rig and how you'll control it (foot controller recommended) and then rehearse with everything. As Matt and the Loop Community team say frequently Ableton is more of an instrument than a static producer of sounds. Treat it that way by rehearsing and becoming comfortable using it before leading your church.
Last rule of thumb that I've learned- keep priorities in order. Your first responsibility is to lead the church. Don't let the tools become an idol. I've been guilty of this more than I'd like to admit. When I pour time and effort into creating and setting up loops and then something doesn't go as planned, my reaction will usually reveal where my priorities are...