Hi, first just keep in the back of your mind that she MAY already know that she has problems with things like memory etc but..........beginning of a friendship/relationship.........she may want to bury them a bit or deflect the things that are going on for her.
But you're right they do really need acknowledging at least. And I'd say that you already have the makings of approaching the situation in the best way. You're going to be approaching it as if you care about her, which is coming across really clearly, as opposed to "putting her under the spotlight". Perhaps kick off the conversation by saying something like "Look, I do really like (?) you but I'm a bit worried that I'm putting a bit much stress/pressure on you, because you know the things you've been forgetting lately: appointments/conversations....well I'm just a bit worried about it" OR even "Do you think (difficult life situation) is getting you down with your forgetting a few things lately? Do you want to talk about it or can I help you a bit with that?" It is doubtful it's that, but hey, it's raising it in a gentle way and opening the doors to discussing what's going on for her.
If she shrugs it of just push gently for if it's happened before and raise your concerns for her, ask if you can help with it at all or if she's tried anything that might help.
I really wouldn't push it too much on this conversation or raise the possibility of any conditions. otherwise you might find her backing away (and you never know it might not actually be a condition!).
But this is going something quite personal to/for her if it is something wrong so just let her have a think about it while knowing that you're being understanding, caring and supportive.
There is a chance that she's going to just tell you to "go away" if she's convinced there's nothing wrong, really worried anyway that there might be, or quite sensitive about it but if your gut feeling is right then it's worth just mentioning.
You may then want to go a bit deeper into conversation another time when you feel that "the timings" right if the problems are persisting. It might take time/more conversations for her to open up more, and I guess she may need to gradually feel she can trust and rely on you before she's telling you more of the true story, ready to accept your help OR ready to hear from you that she may need professional help (if she does). But, I mean it doesn't sound like an emergency situation does it??
Although I've got to say if you have issues of your own and do need to walk away absolutely don't feel guilty about that, you REALLY aren't committed to this, in fact other people in her life will have MUCH more responsibility in helping her if there's anything wrong, and you seriously need to put your "well-being"? first.
You sound like a really caring person though and I really hope things work out for the best WHATEVER you decide to do.
Alison