The speaker has built a life around avoiding pain. By staying in a bubble, they keep away anything new, since new things might hurt. The trouble is that the bubble isn't as safe as it seems: when it breaks, the speaker breaks with it. Protection and fragility turn out to be the same thing.
The middle of the poem makes the fear clear. The speaker doesn't want a broken heart or to be "thrown into the dirt," a phrase that suggests being discarded and humiliated. So they stay put, and the repeated "I stay" and "I remain" make the isolation feel like a habit, almost a routine.
The ending is the saddest part. When someone else is hurt, "a new bubble is blown." The speaker seems to retreat again every time pain appears, even when it isn't their own. The mood is lonely and quietly resigned. The simple, rhyming lines sound almost like a nursery rhyme, which makes the sadness hit harder.