Hi Mihir,
I see. Indeed, you cannot see the search log because the error happened in background, and later when you try manually, the TO gets created successfully, but that means there's no log, which comes up if error happens during bin search.
What you can do, is cancel this TO created in background, and then reprocess the TR in LT04 manually for the entire (initial) quantity(-ies).
In this way you should get the storage bin search log and the same error that's happening in background, and will be able to analyze the system behavior. Why it fails, what is the actual problem.
If that fails... i would advise you to try to find a pattern of some kind.
For example, if you notice that right after the system created TO for partial qty, you try manually and successfully create a TO but for another bin, and it always puts away the remaining qty in another bin, then maybe there is a problem with splitting items in TO.