Since 1.12, I've been regularly fishing from sun up to sun down in game.  In that time I've gone through at least 3 fishing poles, catching around 6 stacks of cod and/or salmon, 5 enchanted bows, 6 enchantment books, 7 name tags, 6 saddles, 3 lily pads, and 3 nautilus shells, and numerous "junk" items.  But in all that time (at least 20 in game days of fishing) I've yet to catch a single enchanted fishing rod.