Shakespeare likely chose not to show Lady Macbeth's death on stage because to do so might prompt the audience to feel some sympathy for her. As ruthless as she's been, we might let her off the hook a little if we had to watch her come to the realization that her best remaining option was to take her own life. If he were to depict it, she would likely be alone on stage, speaking aloud to herself, lamenting her lost hopes, and we could, then, be inclined to finish the play counting her as another tragic figure rather than the person ultimately responsible for the tragedy of others, including Macbeth. It was she who convinced him to go forward with their plan, verbally manipulating him and insulting his masculinity, when he first resolved not to kill the king. Had she not roused his pride, it is likely that he would never have resorted to violence in order to satisfy his ambition. In this way, not showing Lady Macbeth's death also serves to now shift attention to Macbeth.
We've already seen Lady Macbeth, weakened and guilt-ridden, walking in her sleep. We know that, despite her wish to be without regret, she desperately suffers from remorse now. To show her brought to her lowest point would, simply put, be too kind a resolution for her character. So, she dies obscurely, unseen and unmourned by the audience.