Do all routers (nighthawk R7000) eventually start to die? (I'm in desperate need of a replacement.)

the R7000 is a fairly well performing device. 

But all electronics eventually do go bad. 

You could always try to save it by going back to the stock firmware. I've seen fairly decent reviews on it lately. 

Or if you are looking at upgrading, you gave us a budget but didn't say how many devices you wanted to support, what speeds you wanted to support, how big the home, were you looking at mesh systems? Looking at upgrading to AX, etc. 

Details are key as sometimes its better to going with an older generation but mesh system versus upgrading to an AX single router solution