That's been part of the game since Patrician 2. I remember a forum thread on The Tavern where some witnessed pirates crossing land!
It's one of the ways the game cheats.
Try using at least two ships (like you're already doing). When they disappear change the direction of 1 ship, then back again. If you're in a small cluster of AI traders just wait it out a half day. They can reappear a couple of inches (game screen) on the map later. Sometimes they get in a fight with an AI trader and lose, you'll see the ship at an auction or as an AI ship later if it was boarded, otherwise it just disappears.
The problem with the other ship not being able to "see" the pirate can be several reasons. If you right click over a ship, you'll see a white circle. That's how far your other ship can "see". Just lay a course for where he'll be by the time your ship gets there. If there is a small horde of AI traders in the area, they may be blocking your view. Just click and drag a box over the area, then pick him out of the pop-up.