Slitherine

So, I'm going through Sealion '40 and finally the tide has turned. The vaunted RAF has been sent scurrying back to their airfields in the Midlands, all of Her Majesty's Capital ships have been sent to the bottom, the Reading airfield has fallen to the Fallschirmjager, and the Army is preparing to unload the majority of its ground forces on the pleasant Essex beaches despite Herr Churchill's defiant words. So, I start using my light cruiser and remaining destroyers to attack ground concentrations around Southampton, even moving one ship into the port to get closer...

...but next turn that ship promptly and IMMEDIATELY disappears as soon as a weakened British infantry unit tries to move back into the port. No attack, just an instant disappearance and a "+1" to my ship casualty list. The ship wasn't able to back away because a Schnellboote was in the hex next to it. Still, I never expected an instant fail/death without even a defense or something! Is this by design? Ships are incapable of defending a port hex, and if unable to retreat will automatically be destroyed?

I haven`t had it happening against me, but used this "feature" against the AI in some scenarios. Basically if the AI ship is in the harbor and you attack it with a land unit you`ll get a "scuttled"(iirc) message and the ship disappears. I`d imagine it`s the same the other way around.

I think they only scuttle if there is no empty adjacent hex for them to retreat into. Sort of like ground units surrendering.

That's correct - they scuttle if they have no adjacent hex into which they can retreat, otherwise they move into it (like a fully suppressed ground unit). I found the same out the hard way by putting a naval transported elite infantry unit into a port ready to take it next turn - enemy attack 'scuttled' the unit because I hadn't left an escape hex.

Yup, this is all working as intended.
Otherwise ships would be ultimate port defenders as their ground defense is upwards of 10, while the naval attack rating of most ground units is a 1.
Caught in port = death for a naval vessel. Makes good sense too, history has shown time and time again how vulnerably ships at berth can be.

That makes sense, but I can tell you that I'd REALLY like to see something appear on my screen when it happens to me. :-\ There wasn't a "scuttled" message or any other kind of text, the ship just... faded away. So apparently the message appears when you the player does it, but it's not scripted to appear when the AI does it to you. THAT definitely seems like it would benefit from a small improvement. To even realize what happened I had to reload, look at my casualty list, and only then realize the number of number of ships lost had changed. A notification improvement is recommended. (For instance, when it happens to ground units they're nice enough to show "Surrendered", a little pause, the white flag waving, and so on.)