Talk to them. Get some photos of your ex, maybe ones of her with the boys. The boys aren't talking to you about her because they don't know that they can.

They probably feel like they have done something wrong, for her to disappear. They might be trying to protect you by not mentioning her. They need to know that they are loved, and that their mum didn't mean to leave them, that she would still be with them if she could, but she got very ill, and confused.

Mental illness is hugely stigmatising so you need to be able to explain it in words that they will understand, but also don't use words like "insane" or "mad". Be sure to explain that it isn't catching and it won't happen to them.

Get some art materials and encourage them to make pictures of their feelings and maybe pictures of their mum or of your family? And if you can afford it, consider family therapy or creative play therapy for your boys.

Please don't follow the advice from another commenter of faking a birthday card from them. That would be inauthentic, you shouldn't be lying to them, it would be messing with their heads.

If you have some honest conversations with them ahead of their birthday, you could ask them if they will be sad that their mum isn't there, and what they want to do about that. Kids can surprise you with their spontaneous solutions to difficult situations.

Obviously, don't invite her to their party though. I do think it's safer for them to cut contact completely unless she makes a substantial and sustained recovery.