People never go out of style
Interpersonal skills never go out of style, but how they get used will change with technology and industry. In your current work, think about what parts of the job couldn't have been answered by a computer - it may only be 1 customer issue out 20, but that'll be the one they can't replace with a computer. What are the elements of that interaction that made it important that you were there for it? What other industries or work might need that?
Project management, sales, high end customer support all involve some degree of customer relationship skills in the sense that dealing with people who bring money to the table, and who don't see things exactly the way your company/department does can be a big key to success. The difference is that the people who successfully fill these roles may also supplement with some other skill set.
Keep ahead of the tools
A computer is really just a tool, even when it's replacing a human doing a job. Master the tool and you will have a job being the guy who knows the work & what the tool should be doing to do the work. That's generally the key to avoiding the layoff - there's also luck, politics and other factors, there's no absolute. Even in places where the tool really is used by someone with programming skills - your ability to clarify the problem the customer is trying to solve so that the computer can actually solve the problem is a real skill set that has value.
Along with the computer systems that are replacing workers, there will be other changes in the tools that humans use for communications - collaboration is changing at a really rapid pace. 4 years ago, it would have been unthinkable that 90% of my team would be FAR more productive working at home on a snowy day, and the interactions we have outside of the local area barely notice that we're snowed in. But that's exactly what happened today. It's not that we're computer nerds (we are) - the tools that facilitate this interaction are learnable by anyone from artists to engineers - even managers can do it. :)
Things I'd recommend:
- Know conference systems - not just how to run a bridge but how to manage collaboration effectively with a group using one.
- Know video conferencing from a room
- Know how to do a web-based meeting with screen sharing
- Know how to do a video session from a laptop using 2-3 different tools.
This isn't just the tools, this is taking your existing expertise at customer relationship management and translating it to new communication technology. That's where your value as a star will come - most people can limp through setting this stuff and sitting passively through a remote meeting. Many, many fewer can make use of these tools to successfully solve problems and keep relationships positive and thriving.
Use your business skills
Presumably you had some work in your education on markets. Products that need customer relationship managers are products where the customer relationship is a big factor in how a customer makes purchasing decisions. This very well may not be IT related products. I don't feel deeply passionate about much of my equipment - but I do feel passionate about my personal laptop and I go to a human to get help so that a real person can really explain to me the implications of the fixes I need. Probably explains why getting an appointment at the Genius Bar is almost impossible these days. The great folks there are smart, and talented, but they aren't necessarily programmers or people with advanced degrees in CS - their value is that they can facilitate my emotional connection to my computer and make it non-traumatic when I have a problem.
Look for areas where you can add this sort of value - it may not be a traditional role, it may not be the pay you're used to - the company has to be able to recoup the cost of you in the money it makes from customers who need your services.
Keep abreast of retraining options
Never say never about getting more education. IT training runs quite a range from certifications that take 10 weeks and cost a few thousand dollars to degree programs for 100s of 1000s. And plenty of people here would argue that many programmers earn their cred by informal hands on self-training.
When an industry really is dying in the US, it's not unusual to see the US government facilitate some level of training. It's not free necessarily, but you may get far more help than you know.
If you really don't want an IT degree, think about something more radical and look into the training requirements. That one comes down to personal preference, supporting skills and interests that would be too specific to address here - but plenty of people make really radical career changes and yet make fair points that they haven't changed the things they loved about work.