Hello,
If this only happens the first time the services are accessed each morning the problem could be that all of the services have zero instances running and the server cannot activate an instance before the timeout expires. What are the min and max instance setting for each service? How many Arcsoc.exe are running in Task Manager early in the morning?
If all your min instances are set to zero that could be your problem. Try setting min instances to 1 for the most popular services.
All idle services will be shut down after 30 minutes (1800 seconds) with the default publishing settings for an image service.
UPDATE:
I would not recommend publishing all of your image services as shared instances. You should evaluate your services to determine which ones are used most frequently. Those services should use a dedicated instance. The services that are used infrequently can use a shared instance.
I use this python script to generate statistics for my maps services. It should also work for image services:
Bernie.