Yes, you can restrict users from being able to delete ALM entity history.

This can be done via removing a Permission under the Groups and Permissions for a particular user group, within Project Customization.

The Permission to remove is Clear History. Find this under Administration tab which is under the Permissions tab for a specific user group.

As you might not want to limit this feature for all users within a group, recommended best practice is more to restrict specific users. This can best be done by making a new custom user group, editing the permission, and then adding the users you want restricted to this one group only.

A user who is in a group who does not have Clear History permission should receive an error in QC/ALM that shows Error: No Permission to remove an item.