I'm not saying this is the only reason why middle age women are interested in psychics but just to add another perspective. Something I was reading about, here is copy/paste of part of the article.
Menopause represents the new phase in your life - birth into the “wise woman”. Although when the term “menopause” is mentioned, it actually includes “perimenopause” as well, because as the medical community has come to realize, the life transit that menopause represents is actually one that spans 10 years or more for many women. For most of them, hormonal shifts begin in their early 40-s or even mid to late 30-s, whether they notice them yet or not. And with this comes the energetic, psychological, and spiritual shifts that usher them into their wise woman years. In a way, it is a long and complicated transition period.
Changes to your subtle body – your chakras and energetic systems – mirror multiple changes in your physical body. In spiritual traditions that work with the chakras, working with these changes is a big part of the transition into wise woman status – they are part of what enables a shift into a new spiritual perspective and skills. Specifically, it is during this time that you are guided to revisit any themes from earlier in your lives that you have left unexamined, or any wounds you have left unhealed. If you rise to this challenge, you come to own a new relationship to your delicate body, your intuition, and your spiritual selves.
From an energetic technical perspective, this “prompting” often occurs through bursts of kundalini, or spiritual awakening energy, in your chakras. In chakra meditation traditions, ideally the kundalini is brought up gradually from the root to the crown chakra, enabling a smooth spiritual awakening process. During perimenopause, instead there are often sporadic bursts of kundalini (some even connect hot flashes to these bursts, since the kundalini rising often triggers a similar feeling of warmth or “fire”.) Just as your hormones swing during this time, so does your energetics system.
Many women experience these energy bursts as actual sensations of warmth or tingling in a part of their body associated with a chakra. If you meditate on your chakras or work with them in some other way, you may feel active energy in the chakras themselves. If not, you may not be aware of these bursts at all, but instead may see the results of them in the patterns or themes of your life during this time, because these bursts bring forth that which you are asked to heal or learn.
When the energy flows freely through your energetics system, you may experience a flowering of spiritual gifts, particularly of intuition – a key part of the wise woman archetype. Your ability to sense and connect with energies and spirit is magnified. As the reproductive aspect of your physical body winds down, the spiritual aspects of your subtle body ramp up! And this shift is something that can continue to deepen for the rest of your lives.