We hurt our mother's helper's feelings unintentionally, and don't know how to make amends. Any suggestions?

Realtime.... I am a paid caregiver and I feel you are doing the right thing by letting it go... something else is going on here and if she was 'meant to be', she would have picked up the phone and had a conversation with you about all this... on some levels we have to be 'thick skinned' in regard to family, but it sounds as tho you tried to apologize, tho it was never clear what you were apologizing for.... get some one else.... there are great caregivers out there that will communicate with you and not just leave you hanging.... good luck with finding someone else... sounds like a blessing in disguise....

Thanks to all of you. I made a final try by email, no reply. I'm taking captain, Joyce and Jinx's advice and letting it drop. As I go back over the correspondence, I can't find anything that actually calls for an apology from us, much less a gift --- and I've made an apology anyway. So...the lesson I'm taking is that communication should be by phone rather than text or email, so as to identify misunderstandings before they grow into problems.

Find someone else. We have been down this road and gifts, money, etc. will only let them know they have you where they want you. No one is indispensable and if you have to walk on eggsheels, it is not worth it.
We had a caregiving situation with my grandmother. We were 3 hours away and my mother and I started having serious misgivings about this person although my dad just couldn't see it. My dad was sick and wanted someone to help his mom. It was a small town and he knew the family. To make a long story short, this person started saying things to my grandma like, "I can be your daughter" and hanging a family portrait of HER family on my grandmother's wall, putting her foster daughter's photo in the frame with my husband and I's wedding photo and was always, "up against it." Whenever she would do additional sitting, etc. my mom and I always told her to keep her time and that we would pay her. She said her and my grandma had it all worked out.
Turns out, there was a screaming match one day in which she told my grandma she should leave her house to her!
We later found out that there was a registered sex offender at my grandma's church who my grandma befriended. Turns out this woman went to the pastor, the neighbors, etc. but not to us. We had suspicions that something was wrong and started investigating. I asked her why she couldn't even tell the family and her response? "Didn't know what you would say?"
This was someone who always had issues, needed to "be special," needed a bedroom suit, clothes for her kid, etc.
If you have looked over your messages and see nothing wrong, then thank God she is leaving before you have to "bribe" her back to do her job. Trust me, this is how it starts to get more and more money, items, etc. from the family.

I would send a card with a gift - preferably a check. Seriously.

Give it one more try if your mother likes her, but if she won't accept an apology, then you might have to replace her.

if shes too unreasonable to discuss the percieved problem maybe you should let her go on down the road. her reason for quitting may be entirely unrelated to family communications.