hi!
My experience about some error of first access are solved by checking the option: "Periodically check and repair data connections for idle instances" with 30 minutes.
What I have found is that my db administrator stop the database for backup issue and after that the service don't work. With this option all is ok.
Note: the service is for editing data. Service with read only data are oks.
I have a VB script that calls the rest endpoints of my production services first thing in the morning. I put the script into a Scheduled Task to be called in the morning and again every 30 minutes. It works perfectly.
If you'd like it, I can supply the code here. I got it from somewhere in the ESRI support forum land, so it may have already been linked here.