In hindsight, I really could have worded my original question better. It didn't even occur to me that the way I worded the question implied maintaining its position, my bad.

I was just curious if you could get the balloon to maintain an altitude within low earth orbit, without concern for where the balloon actually drifts.

I was imagining a way to get the balloon to behave as a buoy at sea (not anchored), floating above the thicker atmosphere the same way a rubber balloon or raft would drift at sea.