I'd strongly suspect query timeout (meaning the update / insert / delete statement which caused the database growth in the first place).
Looking at the error i'd bet that your query timeout is 30 seconds? growing by 10% means the server has to do perform the query, allocate and format an additional 600 MB of database and complete the transaction all within the timeout period. If your disk is fragmented this could easily exceed that.
BTW, I strongly advise leaving the auto-grow at a (moderately high) fixed percentage for exactly this reason. Autogrow is fine to get you out of a fix when you've run out of space, but is a poor substitute for careful monitoring and active capacity planning. Rather set smaller values (say, 100 MB) as the "emergency autogrow", and give yourself more room (an extra 20% or so) in planned periods when you're not trying to do maintenance and transactions at the same time.