Printer keeps going offline

I have 2 computers networked, office and shop. the printer, Brother 2140, is on the shop. I use Remote Desktop (RD) from shop to access a program on the office computer and want to print to the shop.
I know that sounds confusing. In other words i want to print from the office computer to the shop printer and I do this though RD. I have done this setup for many years with no printing problems. On Jan 5 of this year, the internet stopped working, I called to have the phone company fix it who i have my service through. They replaced my modem/router and said they had to replace a "card" somewhere at a junction box about a mile from here. since then my printer goes offline daily. If I restart the office computer the printer is online and the pending print jobs print. I have uninstalled the printer. I have went into CMD and through the printui have removed drivers on both computers at the same time. re-installed and still goes off at random. through a internet search led me to go into the port properties to un-check a SMNP setting (I think that is the right acronym) but when I try to access that it says that is not supported. both computers have current updates. I have went to Brother website and downloaded latest driver. I keep viruses and spyware in check.
Any ideas would be appreciated.

You might want to log into the router and see what the DHCP lease time is for IP addresses. If it's set to something like expire in 4-8 hours, try changing it to two weeks or never. Restart the printer and computer and see if the problem continues.

Well it was set for 1 day so I changed it to 2 days. I am going to try and see how long it takes to go offline.
Thanks,

you mentioned they replaced your equipment,did you ever,manually set a static ip address for the printer before ? meaning DHCP is disabled so there wont be any communication issues ?

ok, It has not gone off since I changed what travis suggested. If I still have trouble then I should disable DHCP?

Thanks,

With 2 PCs and a printer you don't really need DHCP :)

Like travis0927 said - change your IP lease time to something much higher than 2 days (or never).

yea your can ajust the IP lease time,or disable DHCP and put in your static IP info..thats what i usually do

Well I left out some info not knowing if this will make a difference because I was only have trouble with the 1 printer.:
In the Office I have 3 wifi computers, 2 Netflix devices, 1 USB printer and of coarse 2 smart phones using the wifi.
Hard wired from the office to shop to a switch that hard wires 1 computer and 1 wifi for 2 computer, each has a USB printer and again 2 smart phones using wifi.

It still keeps going offline.

Here is a pic of my setup. I hope this helps. I have searched the web and still not figured it out.

After I restart the "Office" computer, the prints jobs that didn't print are still in the memory and print automatically to the "Dell" or "shopscale" printers depending on which one didn't print.