Well, your tenant hardly pays you for rent and doesn't deserve your free counseling, so I would suggest (and this isn't mean) to tell her you do not wish to discuss her personal life in regards to her nonpayment of rent. I find being a "no BS" kind of person actually gets me a lot of respect. Did you know that (in the US) all of your landlord/tenant relations can be done completely in paper? Write her notice to quit, don't offer to work with her or offer her advice on how she can improve her circumstances (no one likes unsolicited advice, no matter how well intended). It avoids all personal issues. If she calls up sobbing and begging to stay in the apartment or other such drama, then politely tell her you'll address her concerns in writing, request that she leave a telephone message with your office detailing her issue or plan to make a payment. Another option is to hire a rental agent that deals with the people-- you make the decisions) Or convert all correspondence to email, tenant ability to comply factored in.
Okay, that's just addressing the immediate concern. Onto the "real issue"-- that you are not tactful. Don't let this turn into a belief statement about yourself. It's not that you're tactless, it's just that the straightforward manner in which we deal with people puts them off because they're all wrapped up into the social complexities of the situation (she's probably trying to get your sympathy to get more time to pay or go deeper in debt with you, for example. This just really doesn't work on most Aspies. Which I only know of a few in person, a lot on here, maybe others can elaborate on this part).
Don't lose sleep on it! Tact is something everyone else wants you to have, while they can go around with not much at all and be fine. I fall back on polite, respectful, clear, concise. direct for my interactions professionally. Tenant/landlord is a business contract, essentially (not technically) and as such you can treat it that way. Btw, my family has been in the real estate business for three generations and my parents have a property management company as well as being landlords. I'm knowledgeable on US tenant rights/ landlord obligations. Just to clarify, you said you were the "landlord", that implies ownership-- my best advice is to hire a property management company unless you enjoy the hands-on, people oriented business it is. You can still fix the places up if you're into that, just saying leave the people stuff to a professional organization, it really helps.
And yes, we lack that social filter. It's not going to change. But we're also drama-free as a byproduct, enjoy it. (not saying we're not dramatic