My stepmother was always worried about her mother and their doctor taught my stepmother how to walk with her more effectively but pointed out that no matter what, you can't catch someone when they're falling 100% of the time because of the sudden, unexpectedness of it. It's not a "fault" and you didn't fail, I don't feel, no matter if you're a doctor! It happens. It's like any other fall, your own or another's; you help the person up and continue. It's unfortunate but not worth wasting time feeling guilty about.

Thinking of the Veterans Hospital problems and the Congressional Hearing, etc. where it was mentioned one poor guy had been allowed to fall out of bed THREE times. You aren't going to let that happen, now you know it's a problem you'll be more alert and figure out some ways to help (a clicker or bell or some loud buzzer to carry in her pocket so she can "call" for help easier).

It sounds like you are very caring but don't hurt yourself/beat yourself over this; you need your own self regard and health to be effective.