Michael Harvey suggests that you really should only have to "justify" yourself once. This is why he says "try to justify" makes more sense in your example, because of the word "keep", which indicates an ongoing action.
In this way it's like "finish" or "arrive". You normally don't "keep finishing" or "keep arriving", as these are one-time events. You can, of course, "keep trying to finish/arrive" as a continuous action.
I agree with this point, but I can also imagine a series of justifications, repeated over and over, where it makes sense to just say "justify". For example, suppose you disagree with something I did, and I retort:
I don't have to justify myself to you!
Suppose instead you continually reject my reasons, no matter what I say. I could respond:
I don't have to keep justifying myself to you!
I'm not trying to justify myself. I believe I have already justified myself, but you refuse to accept my reasons.
On the other hand, in your example, it's the other person who is offering justifications which you refuse to accept. It makes more sense for you to use "try to justify" because you believe the person has not yet succeeded (and may never succeed) in actually justifying the action.
I don't understand how you can try to justify your actions, as there is no reasonable excuse.
I don't understand why you keep trying to justify your actions with unreasonable excuses.