"The evil that men do lives after them; the good is oft interred with their bones."
Reminder: Starcross lovers is a warning. When your stars align, it's a good thing. When they cross, it's a bad thing.
Also, theory time:
Before, we were talking about how Umi may secretly be depressed and was considering suicide, however that didn't pan out.
What I think is more likely is that their relationship may not be able to work out, and the romantic displays of affection may be prolonging their relationship, but they cannot sustain it. Considering how Rintarou was depressed and holed himself up in his room before Umi entered into his life, he may view her as his savior of sorts, or as the only light in his world, and so the possibility of their relationship not working out or ending on bad terms may affect him to the point where he may regress to a point where he was even worse than that period, and so he may take his own life. (Consider how Rintarou has never checked on his own lifespan.) Considering his history of depression, guilt at being unable to prevent the deaths of his loved ones, and tendency to fall into an existential crisis because of this, I don't think it may be too much of leap to consider this a possibility. What about Umi? Well, I can imagine that she isn't the type that would take guilt or trauma very well, and so I think that she may, finding out that Rintarou took his own life because of her, would also fall into a depression before wanting to "meet" Rintarou again. This would fall in line with how Itsuki says that Umi's life is in Rin's hands and that his actions will be responsible if she lives or dies, as well as his warnings in this chapter about love and how certain actions or lines, even in love, are never justified, and that certain lines should never be crossed.
Will this happen? Probably not, but it's an interesting idea I've been wrestling with.