The Subsidiary field in the Depreciation History record and in the Asset record are custom fields. It is not the same as the standard subsidiary field in the customer/vendor/items. With this, the subsidiary field in the asset/depreciation history record does not behave the same way in other records - like in customers, where you enter a transaction, the subsidiary is carried over.
Please note that this is only applicable to imported depreciation history only (Depreciations created in Fixed Assets > Transactions > Asset Depreciation > will show the subsidiary automatically). Make sure to include a subsidiary record in the CSV file and map it correctly in order to show the subsidiary in your depreciation history.