On your web server, create a script that wakes your services up every 15 minutes or so. Below is an example of a vbs file that the Windows Task Manager runs every 15 minutes:
'declare web app variable, set variable to be an IE application
Dim webApp
Set webApp= CreateObject("InternetExplorer.Application")
'set visibility of the web app, can be set to false to run in the background
webApp.Visible = true
'declare a counter variable as integer, set it to zero
Dim counter
counter = 0
'declare array to hold names of different services
'simply increase the array by +1 and add a new entry for every new service that gets published
dim services(6)
services(0)="MapCache1/MapServer"
services(1)="MapCache2/MapServer"
services(2)="MapCache3/MapServer"
services(3)="MapCache4/MapServer"
services(4)="CompositeLocator/GeocodeServer"
services(5)="Geometry/GeometryServer"
dim map(4)
map(0)="MapCache1/MapServer"
map(1)="MapCache2/MapServer"
map(2)="MapCache3/MapServer"
map(3)="MapCache4/MapServer"
'the following loop uses the REST API and the array to step through each service page
Do while counter < 4
For Each x in services
webApp.Navigate "http://gisweb/ArcGIS/rest/services/"& x
wscript.sleep(2000)
Next
For Each y in map
webApp.Navigate "http://gisweb/ArcGIS/rest/services/"& y & "?f=jsapi"
wscript.sleep(7000)
Next
counter = counter + 1
Loop
webApp.quit
Set webApp = nothing