For the particular friend with the autistic children, I think she gave you her honest answer when she told you "I know you would help me even if you were bleeding out your eyes, but I just can't handle any more on my plate." She was trying to tell you she appreciated what you do for her, and how you are a good friend but doesn't feel she has the strength/patience/etc. to handle watching a couple of kids on top of her own (and I can totally understand her feeling overwhelmed, perhaps, by her own children). In this case, I would say to change your expectations, or, instead of asking her to watch your kids, think about some other ways she can be a good friend to you, and suggest those to her. Heck, if you could line up a sitter for a few hours to watch hers and your kids (or get the hubbies to do it), and take her out to enjoy a show or a quiet dinner, and let the two of you have some fun, that would probably be tremendous for each of you and for your friendship with each other. :)
For your other friends, I would treat them on an individual basis. If the person is someone you feel especially close to, talk to them about it in a non-accusatory fashion, if you're comfortable. If, after you talk to her, nothing changes, you have your answer, because actions speak louder than words.
For those that you're not as close to, give them another chance to say "yes" to helping you. If they don't, well, next time you need to say No, you're not available to help with XYZ thing.
Some people really understand that helping each other out strengthens the bond of community, and others don't. In today's society, we're more fragmented -- instead of having extended family (aka "a village") to help us, we have to rely our spouses (who are often overworked themselves), or our neighbors and friends, many of whom don't understand how helping each other out strengthens things in a community. Church was community for a lot of people, and still is. Of course, there are some people who do understand but don't care or prefer to use/manipulate for their own gain/selfishness.