There's a login check every so often so you can't remain offline forever.
As for getting locked out of your game, the gist of it is that there are two types of bans. If a Bioware employee bans you, your game is fine. However, if an EA employee bans you (an extraordinary case), you'll be locked out.
Bioware and EA moderators have used that as a threat to reduce bad behavior. However, it has never been permanently enforced (i.e. they've restored access the few times it has ever happened).
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