Printer Won't Wake from Sleep Mode

[psmalley-ati]

The printer will go to sleep and cannot be made active again without physically touching a button on the control panel. 
For a network printer this behavior is not acceptable.

On previous models we could disable shut down mode and set the sleep to any number, which worked without issue as the printer would wake up if it received a job. 

Now the printer goes into a shut down mode and we are being told that this cannot be turned off.
What are our options for working around this issue?

[EDIT]
I forgot to include that the printer is connected to our network with an ethernet cable and has a static IP address configured. We have monitoring software that watches the printer and will ping the address and check to make sure the webpage is responsive so we know when the printer goes down. (Shown below with the gaps)
This does not happen with our older HP printers, or any other brand.

[/EDIT]

[amstech-slpc]

We have a HP LaserJet Pro MFP 4101fdw doing the same thing. I turned off all of the shutdown and sleep settings, printer is on the network, but goes to sleep and won't wake on a print job. If we cannot fix this we will send the unit back.

Here's its details

Product Name HP LaserJet Pro MFP 4101fdw

Product Number 2Z619A

Product Serial Number [personal information removed]

Service ID 33261

Firmware Version LOCHSAXXXN002.2226A.00

Engine Firmware 11100