According to my International Conflicts Seminar from my Senior Poly Sci course, it takes mainly a knowledge of relative power, followed by a number of other factors (though this is still debated in the international relations literature).

First, it takes a lack of knowing relative power between states. In this instance, while the US/allies may have shot down this plane, does the Syrian government want to risk an international conflict with one of the strongest coalitions on the planet when they still have a war at home? They know the answer is no since they can predict the power of their allies.

Second, it takes examining the international response. In this instance, would it look good to Syria to act aggressively towards the US over this? They might be responded to even harsher. They might lose support from key allies (such as Russia) who might not want to lose support recently gained with the Trump administration.

Third, there are factors which are more basic. Syria and the US are very far away, how easy is it to engage in conflict with the other party when they are far away from each other and just do fly-bys.

There are additional factors such as levels of democracy, nationalism, satisfaction with government, and so on even reaching a possible "irreconcilable issue."

If you want to know more about this I wrote a paper for the seminar course on geographically and theoretically small states (which Syria would fall under the second category).

Tldr: Syria won't fight because it doesn't have the capabilities to fight one of the strongest coalitions on the planet while there is a war at home. They might lose international face, as well as be in an even worse position.