Yep, definitely shouldn't be dropping and recreating the index each week. Using Ola's excellent maintenance plan to do REBUILD or REORGANIZE is definitely a better choice, and the root of the problem seems to be stale statistics, from a hazarded guess.
If the index is doing well after the creation and is degrading afterwards, the statistics are more than likely no longer good. Tossing in an UPDATE STATISTICS as needed should help to remedy that. From the sound of the problem, there's a good bit of data modification going on that needs to be accounted for.