There is an SLA which has a action being performed at deadline time. Post deadline time it is expected to advance flow by calling FA and move the case forward.

before deadline time reached for the case, the SLA is getting corrupted and going to broken queue (happening sometimes randomly). 

From the XML data I can see the Error: You lack access required to execute Rule-Obj-Activity.tyGetDataPageParameters.

By checking the above activity and its security TAB, Require Authentication is already unchecked. So it doesn't seems there is any priviledge issues.

Also there is no issue of case getting locked also, as if this is the case we can see it in audit history who viewed the case (we have added few features were who ever views and perform certain action on the case can be seen in audit history).

does SLA runs on the access group of the operator who opened the assignment having SLA?

Also I checked access role to object it should be same for all(if it has an issue it should be for all SLA's everytime, but this is not the case).

Re-queuing the SLA from admin studio should work fine, but need to find the route cause for SLA getting corrupted.