There are 2 possible ways the Flows are not triggering on the Sandbox instance after a Minimal Copy.

Let’s look at both the scenarios!

Administration Mode

Let’s get the more obvious options out of the way first. So let’s look at the Administration Mode scenarios where the Background Processes are turned off right after the Minimal Copy is completed –

1. In Power Platform Admin Center (https://admin.powerplatform.microsoft.com/), you can navigate to the environment and look if the Administration Mode is enabled or not.
   
   And if it is, the Background Processes are still turned ON or not.
   
   
2. Now, the Administration Mode can stay ON, the Background Operations however should be Enabled.
   
   If not, then the Administration Mode itself can be disabled entirely which will keep the background operations enabled.
   
   
   But even if this doesn’t help and your Flows are not triggering, below is another possibility.

Callback Registrations in Dataverse

Callback Registration records are created when you create and Save Flows –
Microsoft Docs on Callback Registrations here – https://docs.microsoft.com/en-us/dynamics365/customerengagement/on-premises/developer/entities/callbackregistration?view=op-9-1?WT.mc_id=DX-MVP-5003911

1. Now, the reason the Flows are not triggered are because of the Minimal Copy, the Callback Registration records on the Environment also got deleted.
   So, you can now create a new Flow to query all the Callback Registration records on the environment.
   Add Row Count as 100 or something so that you don’t get a Flow Checker warning. 😊
   
   
2. Now, when you read what Callback Registration records are retrieved, you’ll only find 0 records because all the Dataverse trigger Flows are deleted
   
   
3. And all the other Callback Registration records which should belong to the other Flows (which has Dataverse as the trigger and not other Flows) in my environment are not listed!
   
   
4. And that’s why, the Flows are not triggered which are supposed to be triggered from Dataverse/CRM.
   

Solution

There are 2 solutions to this –

1. First is to Delete the Trigger itself
   
   
   
2. And then re-add the same trigger
   
   
3. And make sure it has all the right steps which it was supposed to have and then Save.
   
   
4. Now, if you Run the on-demand Flow to check the Callback Registrations, 1 record must now have been created.
   And it belongs to the entity which you created the Trigger for. Annotations (Notes), in this case.
   
   
5. And now, if you perform the operation in Dynamics – the Flow will be triggered.
   
   
6. Second solution is to Re-import the Flow or the Solution in which you Flow belongs.

Hope this was helpful! Here are some more Dynamics 365 posts which you might be interested in –

1. Enable SharePoint Online integration Dynamics 365 | Power Platform Admin Center
2. Dynamics 365 Storage Utilization | Dataverse Storage | Power Platform Admin Center
3. Use Hierarchy in Roll Up Fields in Dynamics 365 CRM
4. Filter records in a View owned by a Team you are a member of | Dynamics 365 CRM
5. Get GUID of the current View in Dynamics 365 CRM JS from ribbon button | Ribbon Workbench
6. Dynamics 365 App For Outlook missing on SiteMap in CRM? Use shortcut link [Quick Tip]
7. Import lookup referencing records together in Dynamics 365 CRM | [Linking related entity data during Excel Import]
8. Excel Importing Notes (Annotation) entity in Dynamics 365 CRM
9. Enable/Disable the need to Approve Email for Mailboxes in Dynamics 365 CRM CE
10. Call Azure Function from Dynamics 365 CRM using Webhooks
11. Show Ribbon button only on record selection in Dynamics CRM
12. Accessing multiple occurrences of a field in Business Process Flow using JS in D365 CRM

Thank you!!