Oooh, a sharepoint content database...
Switch the database into simple recovery, checkpoint, checkpoint, checkpoint, (and a few more just to be sure), switch the DB back to full recovery and take a full backup, then you should be able to resume both full and log backups without error.
Then get the storage people to have a look at the IO subsystem for problems.
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: Discussions on DB performance with occasional diversions into recoverability
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