I believe people seriously underestimate how easy it is to run away in this game. With or without loot, anyone can run for an hour. If you get caught with loot and all you have been doing is fleeing, you have only yourself to blame. Here is why it is your fault:
Teleporting Pirate Ninjas - Their are very few circumstances that you or your crew should be caught off guard on an approaching ship. These ships don't come out of nowhere. Unless they traveled through the storm or fog, their should be no excuse. Time and time again on this forum too many people post "This ship came out of nowhere and attacked us" All I ask is, "Did it really come out of nowhere?" The seas are vast and their are very few islands tall enough to actually block sight of a ship. Watch the horizon, having a vague idea of what ships are around you and in what direction will save you a lot of trouble. Even if you are stopped at a ship wreck solo, a glance before you dip your toes in the water should save you from getting caught of guard. It takes 5 minutes for ships to sail from that far. You ain't no mermaid, you shouldn't be under the water that long anyways. On a large island? Take a stroll to the other side, it takes little to no time and will save you in the long run. You have a telescope, use it.
Ship diversity and their strengths - Here's looking at you sloop, a Galleon should never be able to catch you. If you sail against wind you will gain distance. This in itself is already demoralizes most ships to stop chasing. The chase will be delayed for an hour, and very few ships are willing to actually chase that long. Same for the Brigantine.
Delay tactics of the Runner - If you are in a position of being directly behind a ship you are chasing, you are at a disadvantage. In this position, you can be attacked and can't attack back. How you may ask? Through Gunpowder and boarding tactics. If you the Runner have gunpowder, just set your ship going straight and drop one off the back. If you want more of a guaranteed success, just jump with it. The Ship can't afford to veer off, otherwise they lose ground in the chase, so a board is an easy thing. Even if they watch their ladders, they either have to pre-detonate it or let you board. Neither is a good thing, no matter what they do they will take holes and lose players. If you don't have Kegs, just go for an anchor drop. Dropping it once, will cause them to lose a large amount of ground.
Being caught with Loot - If you do any of the previously listed things, you should never lose loot. If you implore any delay tactics and know when to flee cause you see them rolling up in the distance, you should be able to beeline to an outpost. Just sail close to the dock jump off and sell. Be careful not to do it when they are close to cannon off the island. Mermaid back after loot is sold. Ship should be fine if you set its course straight.
Never Anchor - Unless your in a storm, and even then you can get away with not anchoring the most you will do is rotate in place. Learn to lift sails and coast in, this provides the benefit on be able to flee at a moments notice. Its a good habit to get into, learn it now rather then before you sink. It also is a great way to rotate cannons on an approaching ship. Lets be real though, your fleeing not fighting.
Proactive Sailing - The enemy is behind you, their is no excuse to not be proactive on sails. Watch the wind and adjust sails accordingly. If you plan on trying some maneuvers know that you can make tighter turns if you raise some sails. Be prepared to drop them immediately once turn is achieved. Use Rocks, shallow areas (if sloop), fog, volcanoes, and even storms if you are desperate. ( @LimbicFanatic for suggestion)
Resupply in transit - Are you low on supplies? Is this the reason you are running? Time to learn how to resupply while in transit. See those birds flying in the middle of nowhere? This means their is barrels or a sunken ship. Jump ship empty on supplies. Both are a great resource for supplies just mermaid back when the opportunity floats up. Do the same for every island. ( @LimbicFanatic for suggestion)
Get crazy - Passing by a fort? Shoot over and start using the Islands supply of cannons to pepper the ship. You aren't losing anything, the island is. Shoot yourself to the island cannons, then use those cannons to leap frog back onto their ship. Are you able to get onto their ship? Start taking their supplies too. Eat their banana's, use their own kegs against them. Take their rowboat with their own stuff? Why not, keep giving them reasons not to pursue you. If you set the right course for your ship, or you have teammates, your ship will be fine.
Their is very few reasons for the PvE crowd to lose loot to aggresive PvP players. A lot will chime in and say "I am not good at fighting." My answer to this is then you should excel at sailing then. If all your gonna do is flee at least do it right.