You have my sympathies, OP, as I'm in a similar situation. My mother was widowed 25 years ago and has been on her own ever since. She's lucky in as much that I stayed at uni for many, many years, and am single without children, so until I got a full-time job in my late twenties I spent all my holidays at her house. Since I've been working I've not had as much free time, so see less of her.
With regards to Christmas, it's only the last few years when I've decided that I can't, for the sake of my sanity, go down every year. I like having a non-religious time at home and didn't want to feel that I HAD to go every year until she dies. I know this sounds cruel, but I really had to put some boundaries in place. And so I've been staying at home every other year, and will do this year. This isn't totally without reason - me and my flatmate have many pets, and it's hard to ask our elderly neighbour to be responsible at that time of year when there is likely to be snow and ice on the ground. We have got a student in before now, but I don't really like leaving everything in the care of the stranger for a week.
There's no way my mother would come here for Christmas. I have offered, but she wants to go to church and do the religious thing. Fair enough.
There is an extra factor in my situation which is that I'm not an only child. I do have a sister, who lives closer to my mother than I do, yet sees her less. She's not spent Christmas with her for over 10 years. I don't feel it should be my responsibility alone to see my mother is not on her own. Plus there are friends my mother could go to, but won't as then she can't moan she's on her own if I'm not there.
(Sorry, neither helpful nor relevent, but highly cathartic!)