翻译“他一直在琢磨这个问题，直到把它完全解决为止。（to chip away at)

He never stopped chipping away at the problem until he finally managed to settle it.

chip away at是
“琢磨，考虑再三”的意思

He has been pondering this issue until it is completely resolved .

He did not stop working on this problem until he finally chipped it away.

楼主给的短语应该多加了一个at
to chip away 表示铲掉,凿去,逐渐去除 .

He kept chipping away at the problem until he had solved it.