I would think that the most appropriate way to handle this situation is to have a healthy dialogue. When you chat with her about this, are you just mentioning it passively while you are in the car, or do you sit her down one on one and have a genuine conversation about this without any distractions?
First of all, I believe I would offer up positive reinforcement. Something along the lines of "I just wanted to take this opportunity to thank you for all the effort you have given participating with me getting your LTC and going to the range. You know how important I think our SD is, and I think that it is fantastic you join me in the training and activities, because most other wives wouldn't usually participate." (I am NOT saying that women don't EDC, I am just trying to create a statement where the OP's wife feels special. I hope none of the female's on this site take the above statement the wrong way)
After you offer up your own form of positive reinforcement (designed to get her to relax about the subject, and hopefully put her in a positive mindset), begin to gently ask a few questions. "I have noticed lately that the enthusiasm you had for EDC has started to taper off a bit, and I was wondering if there has been anything that has changed your mind about SD/EDC." Or you could say "I want to make sure that I am here for you and support you 100% on your decision, so I am here for any questions or concerns that you have about your EDC."
Pretty much ask questions and get her to talk about HER feelings and opinions of SD/EDC. Let her talk, don't interrupt or make points while she is opening up, and listen to everything she has to say. It is important that she knows that you care about what she is thinking, and you aren't trying to be pushy at this point and tell her that her feelings are wrong.
You then need to make sure that you explain in a calm and non-confrontational demeanor your feelings about her EDC. Do you have kids that you are concerned about their safety? Are you worried about her well being because you love and care for her?
That's it, use this open communication to now have an understanding of what she is thinking and feeling, and now she knows very clearly your opinions as well. Using this as a starting point, you can calmly bring up concerns that she has or problems she might be experiencing, and handle them one by one.
Is the gun too large, or she doesn't have a carry method she likes? Does she find a firearm unnecessary in her mind? Is she hesitant about knowing the laws and regulations well, and feels awkward carrying in public? There are tons of reasons she might not be carrying and I won't assume to know any, so you must ask and find these out yourself.
If you need easy rationalization points . . . I always use cars because everyone drives. She doesn't carry anymore because she doesn't think it necessary : When we bought the car, we wore our seatbelt every time we went anywhere. We didn't expect an accident to happen, but we still buckle up anyway. After a few weeks/months with no accidents, we shouldn't just stop wearing our seat-belts. EDC is just like a seatbelt. It is something you do everyday hoping you never have to use it, but because we will never know when something will happen, the more we use it the better our safety and protection.
Good luck, and keep us updated with how it goes.