Make sure the subproject is set to Read/Write on the Project Properties > Subprojects page. I have found this governs the ability to edit a subproject in MSP.
To change this setting, follow these steps:
1. Open the project to set access to the subproject.
2. Open the Properties menu and click Subprojects.
3. Select the check box next to the subproject, and click Set Read/Write.
The check mark should disappear from the Read Only column.