Connections to a database will not give you the 'database inaccessible' error message. If you're getting that error when backing up, then the database you're trying to back up is not accessible. Don't try things like taking it offline/online without looking at the root problem first, they could make matters worse.
What exactly are you trying to do, what are the exact error messages and what messages are in the SQL error log?
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: Discussions on DB performance with occasional diversions into recoverability
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