There might be a case where the BizTalk360 service account user would not be able to start/stop Host Instances from BizTalk360, Operations -> Infrastructure settings -> Host Instances.
The first step to check for this case would be:
Open BizTalk admin console from BizTalk360 machine as the service account user and try to start/stop host instance. If the user is able to perform operations in the Admin console but not from BizTalk360, then follow the below solution.
1. Adding the BizTalk360 user as local ADMIN in BizTalk server machine.
2. Adding BizTalk360 user as SuperUser in BizTalk360 -> User Access Policy.
3. For the above changes to take effect, IIS reset must be done from an elevated command prompt.
By doing these changes, the user can now start/stop host instances from BizTalk360.