Specs: (Printer) HP ENVY 4500; configuration: local network, WiFi connection.

(Computer) Windows 7.

Description: The printer works fine on restarting. It won't print after long periods of inactivity.

Additional info: I disabled the printer's "sleep" function just in case without success.

My best hypothesis: The printer is in "ad hoc" mode: i.e. it's not permanently connected to computer. I don't know how to test for this. All the interface SOFTWARE has been installed and I think the printer is connected to computer using TCP.

Any suggestions??
If you want to test connectivity and connected via wireless, you could see if it is staying connected a couple of different ways.  One way would be connecting to your router's interface and looking at the list of connected devices.  Another way would be finding the IP of the DEVICE (off a fresh restart) and then pinging it from your PC.  I just tested both on my wireless printer successfully.

In an effort to troubleshoot the actual problem, you could move the printer closer to the router for a LITTLE while and see if it is related.  SOMETIMES if a device loses a signal it doesn't always recover well.  If this is happening frequently in a specific spot, that might be what you're seeing.

Best of luck!