MySQL Subquery hangs / terrible perfomance
The query is slow because the dateindex is used and that is not the best index for this query (or no index at all, please fix the EXPLAIN output). When the subquery is executed, the inventory_ID is already known and the price_type_ID is fixed but there is no composite index that can make this information useful.

Possible explanations for the single query running faster is that you either get cached results from previous execution of the query or it uses different index (and by luck this is a bit more efficient than the dateindex). You have several indexes, on (price_type_ID), on (inventory_ID) but no composite one. So, depending on statistics, the actual parameters and the index chosen each time, the performance will vary.

Try adding an index that will always do an index seek, no index or table scan (and get the price from the index, too, so no additional read form the table will be needed) and thus make both the query and the single query much faster:

ALTER TABLE _inventory_prices 
  ADD INDEX price_type_ID__inventory_ID__date__brutto__IX        -- choose a name
    (price_type_ID, inventory_ID, price_date, price_brutto) ;