I think there are a couple questions that can be evaluated in trying to answer a question like this. I offer them not as one who has all the answers for all of them, but as simple food for thought as a way that we might evaluate our motives and the various facets of such a controversial (as evidenced by the discussion here) moral issue.
First question is, "why are you being threatened?" If it is specifically for the sake of persecution I think it calls for a different response from if you are the target of a random act of violence, for example. I would contend that persecution for our faith is not so much an affront against us as it is an affront against God himself. The flip-side is that man is made in the image of God and therefore is held to be valuable and should be protected against those who would seek to malign God's image as it is reflected in the life of man.
Second question is, "What does our act of self-defense say about what we value and how we view God?" Our actions in any situation offer a statement of what we value and how we view and trust God. What does self-defense in the face of persecution say about how we see God as our provider and protector? I would contend that it implies that we don't fully trust him to be sufficient for our protection or faithful in our death. Efforts for self-defense in response to persecution could also go to imply that we value life more than we value the glory due to God through either our salvation or our death.
However, in the face of random violence, I contend that self-defense speaks to a valuing of life that is in line with the value God has for himself, his image, and the reflection of the same. Genesis 9:6 - "Whoever sheds the blood of man, by man shall his blood be shed, for God made man in his image." God holds himself to be supremely valuable, and mankind has a value placed in our life by virtue of the fact that we were made in the image of that in which God places highest value. To defend life against attack is to affirm the value of life and the even greater value of God.
(Side note that doesn't perfectly fit in with that point but I would suggest is somewhat related: I don't have children, but suppose I do and for some reason there is someone who intends to do us harm. In the face of harm or death my child cries out "Daddy, save me!" and I respond with inaction on the grounds that it is not right that I act in their or my defense. Supposing someone else comes in to stop things before anyone is harmed, what has my inaction told my child about the character and nature of God? What have I told them about how I view or value them? You look at the way the Psalmist describes God moving to act on behalf of his children when they cry out to him for help and tell me that a father moving to protect and defend his wife/children is in some way not keeping in line with the heart and character of God.)
A third question to ask is, "What is gained/lost by my self-defense?" Paul weighs in on this question by offering that to “live is Christ and to die is gain,” but also observes that he is torn between the two options. If I resist persecution, it might secure the continuation of my life for a little while longer, but what of the ways the cause of Christ would/could have been advanced through my reliance on God to enable me to suffer well? Resisting violence may also secure my own safety or allow me to serve as a shield to others, but at what cost to both those resisted and myself (for example, David, for all his military actions on behalf of God and the nation of Israel, was not permitted to run point in the construction of God’s temple because of the blood on his hands).
Overall I find this to be a fearful question to ponder and it is one I’d hope none of us would have to deal with from a position of personal experience (save the case of persecution). For me, I would say that I could not justify self-defense in the face of persecution. However, in the matter of defense against generic violence I believe we should stand against it from a position of valuing life and rejecting those who would act against it
Last thought: I would not consider action and prayer that God would bring something to a peaceable resolution are mutually exclusive. In any case I would desire that God would guide me and my actions, words, attitudes, etc throughout (before, during, and after as the situation allows) such that whatever the outcome he is glorified. At that point it is moving forward in faith, whether it is lowering my weapon, dropping the assailant, or something else altogether, trusting that God is sovereign in all things.
C