All your adjusted timesheets appear to have zero hours in them - so they will not have any slice data in the prj_blb_slices table.
If you remove that table from your SQL (so you just pick up the prtimesheet / prtimeentry records) you should see the structure of the data (the timesheet may not even have any timeentry records?). or put a load of outer joins on the timeentry and slice tables perhaps.
EDIT : oops I see you do already have the outer (LEFT JOIN) , perhaps its the implicit null values that you would get with the outer-joined columns that is causing the confusion - I would break your SQL down a table at a time to understand why the query is not returning data (i.e. adding which table causes it not to return data).
EDIT AGAIN : oops again - I'll try to actually read your post/data before replying this time ; your data is showing the adjusted timesheet (eg the first row, for timesheet id 5070690, prstatus = 5), just that the timesheet is empty (no timeentry rows).
[ If you think the timesheet should have rows, just with no time entered against it, then note that when a timeentry that contains zero hours is on a timesheet that is being POSTED, then the posting job removes the redundant timeentry ]