What are signs that a automobile transmission (specifically a CVT) is going out?

CVT's have drive belts or chains . . . . the chains break and you don't go anywhere. They break because the trans has been abused (most often from shifting from forward to reverse, or reverse to forward whilst the car is still moving - even a bit) ....... or from failure to have the CVT serviced as recommended (drained, filters replaced, new proper CVT fluid with correct anti-friction additives) . . . or someone has put conventional fluid in it.

ADDED: my car with a CVT is a 2006 - 12 years old in June! Really like the CVT - it's smooth, instantaneously responds to hills. It occasionally has a slight jerking sensation in cold weather until it warms-up . . . . has been that way since brand new. They are expensive to repair or replace if they fail: Owners Manual says to service (drain, replace TWO filters, refill) every 60,000 miles - - I have it done every 50,000 miles......and either at dealership or shop that knows CVTs - - - I've asked at a number of quick-oil change places and they know nothing about them, don't have correct fluid, want to flush with a machine: they would wreck it in short order. Costs about $300 to have it done properly - worth every penny because it performs exactly as new.

Slipping

Sluggish acceleration. Car jerks while driving. Most CVTs just fail without warning, car will not do anything when put in Drive or Reverse.