Reproduce steps:
1) Install 7b146
2) remove ScheduleId from "HKLM\Software\Javasoft\Java Update\Policy"
3) Disable javafx update. Which is set "EnableJavaFXAutoUpdate" as 0 under "HKCU\Software\Javasoft\Java Update\Policy\JavaFX"
4) Set the UpdateSchedule (hour) & UpdateMin (minute) reg values to the current time +7 minutes
5) Set Frequency reg value so:
   The regular update schedule is daily. This would be 0x0000XX7F for the Frequency value where XX is set below.
   The critical update schedule is set to the current day of the week + 1.So if today is Wednesday, combining with the regular schedule yields a Frequency value of 0x0000107F
6) Set a LastUpdateFinishTime timestamp that is 1 day before last weeks's critical schedule date/time.So if the critical schedule is set to Thur and the current day is Wed Dec 15th, the LastUpdateFinishTime? should be before Thur Dec 9th.
7) Set UpdateServletURL? so an update is not available. Such as made it point to http://www.sun.com/noMap.xml
8) Start jusched.exe (and wait for the 5 minute sleep if applicable).
   VERIFY jusched.log indicates "Time for a Java Update check" and "No updates available".
   VERIFY jusched.log indicates that jusched is sleeping for ~1 minute for a "Java Update" check.
9) Wait for the indicated sleep time.
   VERIFY jusched.log indicates that jusched is sleeping for ~24 hours for a "Java Update [Critical]" check.

Actual result:
For step 8, get the expect logs.
For step 9, did not get the expect logs. It shows [sleeping for ~24 hours for a "Java Update" check] instead of [sleeping for ~24 hours for a "Java Update [Critical]" check].

Please check the logs in the comments below.

Test case name per QARE requirement are:
AU20/AU20-12-01
AU20/AU20-12-02
AU20/AU20-12-03
AU20/AU20-12-04
AU20/AU20-13-02
AU20/AU20-13-04