You pose quite the dilemma...
The only advice I can give comes from a different but similar situation with some of my grandfather's old fishing gear. To help you through this juncture in your quest I too shall share a story:
My grandfather was an avid angler as well. He did not have the opportunity to drop a line in the water as often as your father, but he did enjoy the reprieve that many of us find in the solace of a tranquil morning on the lake. My grandfather was very old when I was born, and died when I was only 6. My memories of him are faded at best, but I do remember him taking me out in the back yard when I was a young lad and teaching me to cast, reel in, and some other simple basics that mystify children when they first hold a rod in their hands. The rod I always remember him having was a telescopic bamboo job of unknown age or maker. It was meticulously housed in a hard, velvet-lined case similar to a flute or other small instrument. I have no idea of it's value, but those who saw it claimed it was truly an antique and worth more than I realized.
From my modest introduction at 6, and having been raised by my mother and grandmother who didn't really know that much about fishing, I had not returned to the sport until I was 10 or 12. One summer I was shore fishing with his old rod and got my lure caught in the rocks far enough off shore that it was visible, but not reachable. In the inexperience of my youth, I tried...to hard...to dislodge my snag and broke the rod. It broke my heart then, before I even knew what I really had...a link to my grandfather's love of fishing...and my heart still stings a little today as I reminisce about him, this story, and memories of long ago. I do still have some of his lures and various old tackle, but nothing as prized as a rod or reel. These items I rarely use, but often carry for good luck fishing, or simply keep around to remind me of him as I pack my tackle box enjoying a pipe as he used to many-a-night.
I would say that retiring the rod and reel would be a disservice to gear's earned history and disrespectful to your father. That said, I don't believe that such "special" items should be subject to the abuse that we put our day-to-day gear through.
Such things should be kept in working order, perhaps displayed when not in use, but used sparingly. I would take the gear, and memories of your father out on special occasions (father's day, perhaps his birthday, anniversary of his death, whatever day you deem appropriate really) and use them then. On those special occasions share the stories with your children, or fishing mates, and let the memories of your father live on, fish on, beyond his earthly life.
I'd imagine that such respect of spirit and tradition would bring you some of the greatest luck you've ever had on the water...if not...I'm sure that it would warm your heart with memories of time, priceless time, you shared with your dad.
Whatever you decide to do, I'm sure it will be the right thing...just take the time, be open minded, and the answer will come.
Best of luck.