Some providers limit how many map tiles you can download in a set time-frame, and start blocking/banning you if you do too many too fast. Try choosing another map provider.

As to the question: Yes, if you download 10% of the tiles, they're still there. When you re-start, it will skip downloading those tiles as it hits them. At least that was true the last time I used it, to grab tiles. I cached 90% of the area I usually am in, and rarely get tile traffic because of that now.