I know sometimes for dating I struggled (and still do with my hubby) with not knowing how I was going to feel that exact day.
This may sound weird, but this may be worth a shot: have some flowers delivered to her in the office, with a bit longer of a note in it to ask her out. You could say something like, "Hey, I just wanted to know if you wanted to go out with me. I know sometimes your health may make it difficult for certain things, and I don't know what they are. If you to go out, what are some general ideas of what you would like to do, and I could do the planning from there? If I don't hear back from you before (some date), then I will take it that you aren't interested, and I completely respect that."
That gives her some time to think about a reply, not be put on the spot to come up with an answer if her first reaction is to just say no. It also lets her know that you are aware of her health and want to be considerate, but you think she's worth doing the planning for. It also gives her an out if she wants to say no because she's not interested.
Not sure if that makes much sense, but it seems a gentler approach with a woman who may need that right now.
"For this thing I besought the Lord thrice that it depart from me. He said, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities; I take pleasure in infirmities, reproaches, necessities, persecutions, distresses, for when I am weak, then am I strong" 2 Cor