Seems like you need to recreate the distribution service folder.
1. Stop services.
2. Backup the folder c:\programdata\qliktech\distribution service and remove it from there or change its name.
3. Restart services.
That will create a brand new blank area for you to assign schedules again. The drawback is you need to create tasks again.
If the problem still persists; you may need to upgrade the QVS version. I assume it is old since we used to come across to that a lot in the early versions of 11.
I have got this kind of issue when we upgraded to QV 11 from 10.
1.1 Schedules are showing last run time as Never under status tab in QMC
Modified URL as below under system--> setup-->Distribution Service--> general.
URL has to be like http://publisherhostname:4720/qtxs.asmx
Hope this helps,