You can disable users from deleting the browser history by folling this Microsoft Technet article: https://technet.microsoft.com/en-us/library/dd349812.aspx
You need to type gpedit.msc to open the Group Policies Editor in the Run window of the user and turn off the values for deleting browsing history.
To quote from the above mentioned website:
If you don’t want users to be able to delete their browsing history, form data, or passwords, you can enable the following group policy settings located in both Computer Configuration\Administrative Templates\Windows Components\Internet Explorer\ and User Configuration\Administrative Templates\Windows Components\Internet Explorer: Turn off “Delete Browsing History” Functionality Turn off “Delete Forms” Functionality Turn off “Delete Passwords” Functionality