If you would loose the battle and at least one unit retreats to the initial Port Castle the ships in the port would survive as well. Which is kind of strange I think.
Then it’s just a bug here. When you leave the area without leaving a token behind the area is temporary uncontrolled, thus leading to the ships getting destroyed immediately (or converted back to the capital owner in case).

When they are not destroyed here I guess the ship handling just happens in the wrong timing window: after battle when units possibly have retreated back to the starting region, leading to the ships not being destroyed. If so this is a bug.

There are some rules which contradict each other.
This issue was discussed a few times already. Even if you technically left your original area marching out to attack another area, your units are still bound to the area you came from since it is not allowed to occupy an area with two houses at the same time.
You should lose your ships regarding the rules, but since you never left by winning the battle ships stay, at least on thronemaster.net
That is not true and explicitly clarified in FAQ:

Q: If a player marches all their land units out of an area (but not their home area) that is connected to a Port with their ships, and in doing so chooses not to leave behind a power token, what happens to that player’s ships in the Port?
A: Ships left in a Port that is connected to an uncontrolled land area are immediately destroyed. If the land area connected to the Port is an enemy home area, those ships instead may immediately be replaced with ships of that enemy’s House (as per the rules under “Taking Control of Enemy Ports” on page 25).

Together with

Q: When a player resolves a March order, if they march all of their units out of another player’s homearea and do not leave behind a power token to establish control, where must they retreat if they were to lose the ensuing combat?
A: They would have no legal target for retreat and would thus be destroyed.

it's clear that units leave the area for the battle and are not bound to their starting region anymore. For the same reason you are asked to leave a Power token behind BEFORE you start the battle. If you could do it after battle you
wouldn't need to leave a Power token in case you lose. From my point of view the situation is clear.