If you want stability stay away from field work. Not to say that some people don't work steadily, their entire career, for one shop, but this is more an exception than a norm.
I have friends that enjoyed working in the shipyards, and know others that have spent many years working in pipe fab shops. The pay is a little lower, but these jobs are better layed out, safer, and more stable.
Union apprenticeship in most of your larger cities will have a fair amount of work (always for willing apprentices) and good compensation and benefits. Once you reach journeyman status you are more expensive and often times will be layed off or furloughed more frequently. There are opportunities to travel when work gets slow and if your willing to go you can normally find a paycheck somewhere, however it also creates big strains on a family.
performance, turner, bay limtied, s&b all got some jobs going on. they out of baton rouge