As promised, the solution to at least part of the problem. Unfortunately it shows up my lack of attention to detail and willingness to assume without the facts.
As it turns out, the starter and the domestic batteries are connected and are charged when on shore power.
My domestic batteries are easy to access (under the back cabin floor) and are maintenance-free. My starter battery is in a box under the bed and is difficult to get at. I had assumed it was also maintenance-free - certainly it had not been touched in the five years that I have owned the boat. In fact I have never even looked at it.
It turns out that it was a standard lead acid battery which, having survived this treatment for far longer than I deserved, eventually boiled dry.
I know that many (most) of you will think "surely if he had battery problems he would have at least looked at the battery" - well no, I didn't, I made some assumptions. As often will be the case, these were wrong and I have learned something. Alas learning something from the previous problem doesn't seem to prepare me for the next one!