I don't know how to fix the page break problem within the subreport, however I have had enough experience troubleshooting subreports that I have learned that sometimes it is easier to approach the issue from another way.
There are situations like you are experiencing that I will create a query that has both the report and subreport data in it. That way you don't have to use a subreport. Doing this will avoid all the flaky issues that might occur when you use several subreports or nested subreports 2 or 3 deep.
The gist of the approach is to create a query that is no longer normalized. So for example if you had a Project table and a Project Tasks table the data might look like:
ProjectID, ProjectName, BeginDate, etc.
1, Project1, 02/18/05
2, Project2, 02/15/05
ProjectTaskID,ProjectID, TaskName, etc.
405, 1, Remove Something
406, 1, Add Something
407, 2, Do Something Else