The network connection to the printer has been lost.

Question

I have reserved an IP address for my printer in my router. I routinely get the following message in Windows 8.1 64: "Scan to computer is no longer activated. The network connection to the printer has been lost." Also, when printing, sometimes the printing cuts out (i.e. half the job).

Answer 1

bcbrewster
Well, then the issue remains vague and you must track down a reason for the disconnect -- the connection is breaking between the printer and the computer -- and apparently, from your description - this even happens on occasion during a print job.   
Event Viewer Logs
If the computer is aware of the cause, you might find it in the Event Viewer logs.  There is a wealth of information packed into the daily logs kept by the system on a great many of the computer's actvitiies.  The trick is to 1) find the log containing the information you seek, and 2) Decipher what you have found. 
Reading Event Viewer logs is part science and part art.   I cannot tell you precisely where to look because I don't know where your problem is located. 
I can give you some information on how to get started:
Windows 8 Event Viewer
===============================================
Disconnections
Disconnection can be caused by a number of things, most of which you have probably already read about in your searches:
The issue could be due to the need for a Firmware Update.  You would have noted this during your previous Troubleshooting - and the only Firmware update for this model is dated 2013. 
HPCOM_HP_ENVY_4500_series_x86_000_003.exe
Reference:
HP ENVY 4500 e-All-in-One Printer
=======================================================
Possible causes for connection issues include and are not limited to:
The router should be no closer than three feet (about a meter) to the printer - too close is as bad as too far away
You can try moving things around -- even a few inches one way or another can help
Weak antennas or single antenna routers cannot be "magically" made better; these routers might perform better when placed higher in a room rather than lower.  That is, place the router high on a shelf instead of low in a cabinet
Try changing the channel -- 6, 11 might work better
Try using a static IP outside of the DHCP range of the computers on the same network.
==========================================
References and Power Options
IF you are running a notebook
and if the notebook is running on battery
and if that notebook is running wireless
and if the notebook is having trouble staying connected
THEN:
Control Panel > icon view > Power Options >
Under Choose or customize a power plan >>
Under Plans shown on the battery meter >>
Next to HP Recommended >> Click Change Plan Settings >
Click Change advanced power Settings >
Scroll down and Open Wireless Adapter Settings >
Click Power Saving Mode >>
Adjust Power settings for On battery and for Plugged in Options
Click on the current option to enable the drop down menu and see the available settings wireless adapter / system
If you have been having trouble with running wireless on battery, consider setting the wireless to maximum performance while on battery.
Understand this uses more battery resource.
Click OK to save and exit
=================================
References:
Static IP Address for Printer
Settings to Improve Wireless Connectivity
Click the Kudos Thumbs-Up to say Thank You!
And...Click Accept as Solution when my Answer provides a Fix or Workaround!
I am pleased to provide assistance on behalf of HP. I do not work for HP. 
Kind Regards,
Dragon-Fur