Still going with the same force, not having weakened at all. The word is used for things that people would normally expect to die down over time — rain, wind, fighting, criticism, demand, enthusiasm. That expectation is the heart of it: you only say the storm continued unabated because storms usually pass. Grammatically it is odd and worth watching. It nearly always comes after the verb rather than before the noun — "the violence continued unabated", "interest in the case remains unabated" — and it is glued to a small set of verbs: continue, rage, go on, remain, persist. You would not normally say "an unabated storm" in front of the noun, even though the meaning would be clear. It belongs to news writing and formal prose; in conversation people just say "it didn't let up" or "it's still going strong".