You need to build a custom logic to achieve this requirement.
Woraround 1:
Create a program to check your table while deleting of existing records, it has to write those deleted records into another table with X flag.
You need to create table based generic datasource on this deletion table and load to the same infoprovider in BW side. So, whatever has been deleted in table, will come with X flag in BW side. Thus, you should exclude those records in reporting by excluding X flagged in queries.
Workaround 2 :
If you are sure that the data in table is simply getting deleted, then you can delete the loaded request everyday before extracting new data request.
We have "Delete Overlapping request" process type is for Cube.
We also have "Delete entire contents" of DSO. You can make use any of them as per your infoprovider type.