A challenging situation.
You've got a very fine line to draw here. On the one hand, from a purely business perspective, having a customer who is literally driving other customers away is something you can't tolerate. If - as you say - the situation is that bad, then I really don't think you have any choice but to do something.
On the other hand, I'd recommend strongly against getting too deeply involved in whatever personal, financial, or psychological issues may be troubling this woman. You are a restaurant manager - not a social worker. And even in a small community, where "everyone knows everyone" its best to let people for things out for themselves.
My recommendation would be to keep the thing as businesslike as possible. Instruct your staff that the next time the woman shows up (in a malodorous state) you need to be alerted immediately. Take her aside, to whatever private area you have, and tell her firmly, but politely, that she cannot dine their until she takes care of whatever is causing the poor personal odor.
How you word that is key: You don't want to imply its because she doesn't bathe (she may have some medical issue thats causing it.) You also, strangely enough, don't want to mention that other customers have complained about her (even if they have.) That may prompt arguments about people "ganging up" on her, and other paranoid reactions. Simply say that, until she "takes care of" or "addresses" the issue, she may not visit your restaurant. You need to stay away from words like "stinky" - simply say that you have noticed that she has a "body odor that is unacceptable" in your restaurant.
She's probably going to be upset. Prepare yourself for that. You may also wish to have available the telephone numbers of various local agencies: medical, mental health, Government or Charitable aid, etc. If this person is without their own personal transportation - you should offer to pay for a cab ride home, on the understanding that she not return until the issue is resolved. Lastly, you should make it clear (if you get the chance) she will be more than welcome to dine with you again once she's "taken care" of the situation. You might (if you are a real Saint) offer her a free meal if she does. (Just don't tell her you'll give her a thorough smell-test before going through with it.)
Good luck. The fact that you chose to ask this question tells me you are decent person who is (rightly) troubled about having to deal with such a delicate situation.