Hello, Jolaine;
Have you worked through this issue? If not, please look in the CA configuration database's tblCustomer table for the status of the CA customers showing as having the service stopped and relate the StatusID shown to the tblStatus table in the config db to see what that statue actually means. Also look in Task Manager on the CA server to see if you have 1 instance of the AcceleratorService.exe process for each CA Customer on that server plus 1 for the Remoting option (i.e., 10 CA Customers would have 11 instances of AcceleratorService.exe process running).
If you don't see the right number of AcceleratorService.exe processes, the you have some CA customers that are not running their background tasks, which also means they won't be running any searches.
If you find the tblCustomer table shows these customers are actually running, then you've encountered an ASP.NET cache refresh issue that can be addressed by implementing the DisableLazyContentPropogation registry value per TECH124694.
Let us know how things are going and what you find with the information above if you're still having the problem. We'll do what we can to get you running again.