O rose thou art sick (1)
Sickness isn't always associated with death, but the ominous tone of the poem coupled with the fact that nearly half of it (4-8) is concerned with violence, death, and maybe even rape suggests that "sick" means "sick and about to die." The poem even implies that the sickness is some kind of perverted pregnancy brought about by the worm's "dark secret love."
Has found out they bed Of crimson joy (5-6)
Although they are not ostensibly about death, there is something ominous about the tone of these lines; it is as if the rose is hiding something important which the worm has just discovered and plans on stealing. Since the rose gets destroyed by the end of the poem, it's hard not to read this moment of penetration as a foreshadowing of death.
And his dark secret love Does thy life destroy (7-8)
The poem establishes a connection between death ("life destroy") and "dark secret love." "Love" only leads to death when it is "dark and secret," so perhaps there is a kind of love that isn't "dark" or "secret" and doesn't lead to death.