Start a workflow for a list item that was created by someone else

What settings do I need to change so that I can start a workflow for a list item created by another user?

I have a SharePoint 2013 workflow (let's call it LSR Status Workflow) that is associated with a list (calledLSR List). When a user creates an item in the LSR List, it automatically starts theLSR Status Workflow. That is what I wanted, but sometimes I make changes to the workflow (via SharePoint designer) and then I would want to terminate the existing workflows that are running and restart them.

When I try to start a workflow for anyone other than a list item that I created, I get the following error:

Retrying last request. Next attempt scheduled in less than one minute. Details of last request: HTTP NotFound to https://publishing.web.company.com/sites/mysite/_vti_bin/client.svc/web/lists/getbyid(guid'1f844b8f-19aa-4587-bcc2-dfb7085f36b5')/Items(31)
 Correlation Id: 8efc5304-f0a3-90f6-8ece-6875bf811869 Instance Id:
60c83aae-5c25-4ee8-9c85-c64958ba701e

Then when the workflow is finally suspended after it keeps retrying, it reports the following error:

RequestorId: 8efc5304-f0a3-90f6-0000-000000000000. Details: An unhandled
 exception occurred during the execution of the workflow instance.
Exception details: System.ApplicationException: HTTP 404
{"Transfer-Encoding":["chunked"],"X-SharePointHealthScore":["0"],"SPClientServiceRequestDuration":["36"],"SPRequestGuid":["8efc5304-f0a3-90f6-9bbd-d18d4d90af1b"],"request-id":["8efc5304-f0a3-90f6-9bbd-d18d4d90af1b"],"X-FRAME-OPTIONS":["SAMEORIGIN"],"MicrosoftSharePointTeamServices":["15.0.0.4551"],"X-Content-Type-Options":["nosniff"],"X-MS-InvokeApp":["1;
 RequireReadOnly"],"Cache-Control":["max-age=0, private"],"Date":["Tue,
10 Feb 2015 22:36:44
GMT"],"Set-Cookie":["BIGipServerpublishing-blv-80-pool=2825582466.20480.0000;

path=/"],"Server":["Microsoft-IIS/7.5"],"X-AspNet-Version":["4.0.30319"],"X-Powered-By":["ASP.NET"]}
 at
Microsoft.Activities.Hosting.Runtime.Subroutine.SubroutineChild.Execute(CodeActivityContext
 context) at
System.Activities.CodeActivity.InternalExecute(ActivityInstance
instance, ActivityExecutor executor, BookmarkManager bookmarkManager) at

System.Activities.Runtime.ActivityExecutor.ExecuteActivityWorkItem.ExecuteBody(ActivityExecutor
 executor, BookmarkManager bookmarkManager, Location resultLocation)

If I created the list item, I can stop it and restart it without any problems, but this is not the case for list items created by someone else.What settings do I need to change so that I can start a workflow for a list item created by another user? I am the owner of the SharePoint site and am able to make changes to permissions if needed.