Question: Here are the steps to reproduce this:

1. Post a question (make it a good one)
2. Wait for a reply
3. Wait for it to get an up vote
4. Down vote it (or wait for it to be down voted; although I have not tried this)
5. Try to delete it

Don't forget to undo your down vote, unless you really meant it.

Edit: 
As for the bug being there by design, as it has been suggested, I'm not sure. The design allows deletion of a reply by the OP if the reply has no up vote. It follows that the design should allow such removals if the answer has only down votes.

I have not tested this and don't know if deletion is possible in this case. But it would be very odd and contradictory if the system did not allow that.

What if it the reply had a net negative vote?
Would the vote of the OP be counted in this case?

What if all votes were negative except one up vote?

There's obviously something about deletion of questions with a single reply of questionable quality that is not truly answered by the service agreement or the FAQs. 

How does it work?
How is it supposed to work?

Answer: 
The provisions in the terms are specifically designed to provide some protection from the time that people spend writing answers going to waste. At some point, your question becomes more than just *your* work, and more than just *your* time that would be wasted if it were to be removed. 

The concept of reputation loss aside, a great way to make people hesitant to contribute answers is uncertainty that there's any permanence afforded to them. Many flock to us because our system naturally elevates *good* knowledge in a manner that makes it easier for anyone seeking it to find - this is the antithesis of things like usenet, and classic forums. It's important for us to protect this premise in a manner that allows us to guarantee it to our users. 

There can be exceptions. If you have a *compelling* reason to have your question deleted, where disassociating it from you entirely after editing out sensitive information and deleting any revision where it was visible would not work, we're open to listening. One needs only to [contact us](https://meta.stackexchange.com/contact) to discuss this. Our answer is *very* likely to be no, but will usually be accompanied with an offer to help make the existence of the question no longer cause problems for you through other means.

Our system is quite complicated as it's *currently* explained, we're very unlikely to break out all of the special checks and contingencies we have in place to prevent users from missing the *intent* of a feature in favor of finding a way to work around it. It's sufficient to say that we've thought of a few scenarios that we should probably check for prior to deleting something, up to and including automatically notifiying moderators if an abnormal number of any given user's contributions are self-deleted.

And this leads to the simplest thing of all - if you feel that something isn't right, or the system won't let you do something that you feel strongly that you *must* do, contact us and let us know. We're humans, we listen, and we will try to find a way to help.
The answers are posts *too* and if those have a positive score there is more than one post to consider here. The Question and the Answers together form a collective work now.

As such the system will not let you delete your own question if it has 1 answer with *an **upvote***, or if it has more than one answer in total.

The emphasis is on *upvote* here. If the single answer has received even just *one* upvote, you can no longer delete your question. The moment the community feels the answer has merit, there is a collective work and you can no longer *self* delete.

It then no longer matters what the *score* is of the answer. Your downvote bringing the answer back to 0 does no negate the upvote already in place.

Note that even if you *could* have deleted your question, the community may not agree with that deletion and *undelete* a post again. This is allowed per the [terms of service](https://stackexchange.com/legal):

> 
> Stack Exchange reserves the right to remove any Subscriber Content from the Network, **re-post to the Network any Subscriber Content removed by any Subscriber or former Subscriber** [...]
> 
> 
> 

That's because *the moment you post* you are licensing the content to Stack Exchange:

> 
> You agree that all Subscriber Content that You contribute to the Network is perpetually and irrevocably licensed to Stack Exchange under the Creative Commons Attribution Share Alike license.
> 
> 
> 

For you as question asker there is the option to be *disassociated* with the post. Your name will no longer be on the question, but the question will live on, owned by the community.

See [How do I remove my name from a post, in accordance with CC BY-SA?](https://meta.stackexchange.com/questions/96732/how-do-i-remove-my-name-from-a-post-in-accordance-with-ccwiki)

You can always [contact](https://meta.stackexchange.com/contact) the community team if you have a problem with how this all works; it is geared to protect *all* contributors, but sometimes you may have a good and compelling reason to not be associated with a post.