Dang. Sounds like she needs some R & R.
There comes a time when it's important to take care of yourself as well as you take care of everyone else... but I understand her wanting to try her best. I just think in this case Ms. LaBelle needed to sit it out, go take a warm cup of soup and sleep.
Audiences feel cheated, but I think a sick day off is better than a having a performer drop dead from exhaustion.
It's really hard when you're 62, sick, and cold. I hope Ms. LaBelle gets to feeling better so she can belt them out on a better day. Better days do come...