Restrict users from modifying datasources in SSRS
I'm going to guess that you are running SSRS in Native mode rather than SharePoint integrated, and that you are using the pre-defined roles to grant access to users. If you want to post more information about the version of SQL Server you are using and the security role these users are in, I can update my answer. For now, try this. 

There are pre-defined security roles in SSRS: 


Content Manager
Publisher
Browser
Report Builder
My Reports
System Administrator
System User


I'm going to guess that these users are currently in the My Reports Role.  This role is allowed to do quite a bit, including manage data sources and manage reports.  This means these users can create delete, view, and modify data sources. 

You might want to consider creating a new role that has only the item-level permissions you want.  You can find the list of item-level tasks here. You basically want to include all of the item-level tasks included in the My Reports role, except Manage Data Sources. You could also modify the My Reports role to remove this one item rather than creating a new role.