SQL Server 2008 R2 hasn't been supported since ArcGIS 10.3.x. Are you running 10.3.x or older on both the server and desktop? Also, ArcGIS 10.3.x has reached mature support status which means there won't be any updates, patches, or fixes for it (with an occasional rare exception).
As you describe the situation, you aren't really sure the spatial index is disappearing, you only know that recalculating it addresses your issue. In your original post, you state that the data is being manipulated by a script. Does that script recalculate the spatial indexes when it completes?