Mom won't accept non-family help!

My mother lives in another state and has no relatives who can regularly help her with things she is beginning to need more help with. She sometimes needs transportation to the eye doctor if she is getting her eyes dilated. She is having more trouble keeping her home clean and shopping for heavy items. I have offered repeatedly to set her up with services to help with these things and she has some money but she refuses it all. Just recently she postponed an important eye doctor appointment where she was due to get a regularly scheduled important injection she needed because her sister was unable to drive her that day. She would not call a cab even though she could afford it. This has been a problem throughout her life but as her needs increase and there is not local family there able to meet those needs she MUST begin to accept paid help. But I can't make her do it! She will neglect herself grievously rather than accept outside help. I've decided at some point I'll just have to call social services but then her precious independence and privacy will be shattered and she may never forgive me. If we become estranged then I truly can't help her at a distance and for right now moving her to my location is not an option. What can I do???