IANAL. This is not legal advice, just my opinion.
Do you think the chance is really zero that the armed robber won't turn around and shoot you as he's leaving? IMO, he is a deadly threat until you are in a place where the robber is not able to shoot you. Thinking otherwise could get you killed.
Emphasis mine....
Sec. 9.32. DEADLY FORCE IN DEFENSE OF PERSON. (a) A person is justified in using deadly force against another:
(1) if the actor would be justified in using force against the other under Section 9.31; and
(2) when and to the degree the actor reasonably believes the deadly force is immediately necessary:
(A) to protect the actor against the other's use or attempted use of unlawful deadly force; or
(B) to prevent the other's imminent commission of aggravated kidnapping, murder, sexual assault, aggravated sexual assault, robbery, or aggravated robbery.
(b) The actor's belief under Subsection (a)(2) that the deadly force was immediately necessary as described by that subdivision is presumed to be reasonable if the actor:
(1) knew or had reason to believe that the person against whom the deadly force was used:
(A) unlawfully and with force entered, or was attempting to enter unlawfully and with force, the actor's occupied habitation, vehicle, or place of business or employment;
(B) unlawfully and with force removed, or was attempting to remove unlawfully and with force, the actor from the actor's habitation, vehicle, or place of business or employment; or
(C) was committing or attempting to commit an offense described by Subsection (a)(2)(B);
(2) did not provoke the person against whom the force was used; and
(3) was not otherwise engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic at the time the force was used.
(c) A person who has a right to be present at the location where the deadly force is used, who has not provoked the person against whom the deadly force is used, and who is not engaged in criminal activity at the time the deadly force is used is not required to retreat before using deadly force as described by this section.
(d) For purposes of Subsection (a)(2), in determining whether an actor described by Subsection (c) reasonably believed that the use of deadly force was necessary, a finder of fact may not consider whether the actor failed to retreat.
Sec. 9.34. PROTECTION OF LIFE OR HEALTH. (a) A person is justified in using force, but not deadly force, against another when and to the degree he reasonably believes the force is immediately necessary to prevent the other from committing suicide or inflicting serious bodily injury to himself.
(b) A person is justified in using both force and deadly force against another when and to the degree he reasonably believes the force or deadly force is immediately necessary to preserve the other's life in an emergency.
Sec. 9.42. DEADLY FORCE TO PROTECT PROPERTY. A person is justified in using deadly force against another to protect land or tangible, movable property:
(1) if he would be justified in using force against the other under Section 9.41; and
(2) when and to the degree he reasonably believes the deadly force is immediately necessary:
(A) to prevent the other's imminent commission of arson, burglary, robbery, aggravated robbery, theft during the nighttime, or criminal mischief during the nighttime; or
(B) to prevent the other who is fleeing immediately after committing burglary, robbery, aggravated robbery, or theft during the nighttime from escaping with the property; and
(3) he reasonably believes that:
(A) the land or property cannot be protected or recovered by any other means; or
(B) the use of force other than deadly force to protect or recover the land or property would expose the actor or another to a substantial risk of death or serious bodily injury.