Mom wants her own credit card but last time I gave her one she lost it. Any suggestions on how to appease her?

Okay, more info would be helpful. We've all misplaced credit cards at one point or another. But my guess is that she has dementia?

Do you see other symptoms of forgetfulness? If so, is she still driving?

Perhaps it is time to take away the keys and take her shopping.

Hello lkmichael63: I heard a report on a credit card that parents were using for their teenagers. The trick to it is the parents put on any amount they choose, and wherever/whenever the teenagers go to use the card it signals the parents, where? how much?..., and if the parents did NOT want to approve the purchase they could decline right on their cell phone. Keeps the teenagers honest, and the parents watch on them. Not calling your Mom a child, but if that helps.

Would a pre-purchased gift card with VISA or AM EX work for her needs? You don't even need to tell her what it is. Just call it a credit card, since it works just like one.

If she's cognitively able to use the card, then be sure to write down all information about it, including number and the customer service number on the back. At least you can do damage control. Or, you could try a secured card that has maybe $200 on it. Yes, you could be out that money if she lost it, but no danger of others charging more.
If she just wants it to carry it around but doesn't use it, give her an outdated one. I did that with my dad. He wanted a CC, so I gave him cards that were no longer good. That satisfied him.
Good luck,
Carol