How are you doing the shrink? You could try DBCC SHRINKFILE with TRUNCATEONLY. That will release space after the last allocated extent. It should be faster. The problem is if you have a lot of data deleted and the pages are not reorganized you might not get the space savings you realize.

This is probably something that will either need to be scheduled during a maintenance window with authorized downtime or look for another solution, like growing storage of the volume data files are stored on.