Stu, I am around the boat about two or three times a week, and like a cold beer after a bit of work. Are you suggesting it stays off, and I just turn it on the night before a trip? Isnt that much more wear on it rather than just leaving it ticking over?
Steve answered it one way, which is quite logical. We have a C34 skipper who has his office 200 yards away from where his boat is docked, so he, like Steve, is on the boat, checking things out, on an even more than "regular" basis.
If all you want is a cold beer after work (and I've heard that often), then stop at a 7-11 on the way there. Two benefits: 1) you'll always have a cold beer; 2) you'll build up your beer reserves on the boat!
Seriously though, your corroded terminal is a PERFECT example about how a boat can kill itself if you remain plugged in when you're not there "for a good reason." I personally don't call having a cold one a good reason.
What would I call a good reason? Making sure your bank is completely topped off. And even after a daysail with a fridge running you've taken maybe 30-60ah out of a reasonably sized house bank. That takes more than the hour you might spend plugged in when you come back and tidy things up, it takes overnight to get back to 100%. I charge up and then disconnect.
This is NOT an either-or, my-way-or-the-highway thing.
It's a
boat management issue. FWIW, many of us have been having this discussion for decades.
Here's my approach:
Unless I'm going out the next day and think (for management reasons) I need to plug the boat in overnight to assure a full bank for the next day or two's cruise (I anchor out everytime I go out, got too tired of doing the mainsail cover twice a day on & off

), I never leave the boat plugged in. Since I eat on the boat when anchored, I'm willing to lug the mayo (!!!

) and have a ton of ketchup things from In & Out on board.

I also have a squeeze bottle of (NOT French yellow) mustard on board in the pantry, not the fridge. Although I must admit it stays better here on The (cooler) Bay than it would on Steve's boat in The (much hotter) California Delta.
I just don't want to face what you have with your battery connection. My boat's worth more to me than a cold beer. BTW, I turn my fridge on when I get on the boat and in a half an hour or so, the two cold ones I put inside the evaporator get cold enough. I also spent a few days of our recent vacation in England and can drink a warmer one if need be!



Don't get me started on "ice" in drinks in England, the glasses are so danged small it can't be called a drink!

I also bring ice from home for drinks after the anchor is down for the first day of any cruise, our fridge makes ice in the vertical trays just fine overnight for anything longer.
The other thing is, as I understand it, you risk sulfating the batteries if they're kept on float forever.
Your boat, your choice. There is no "right" answer, but from this experience, I'm sure you've learned a lot, perhaps the hard way, but glad there was no other damage.
Running a boat fridge isn't like your fridge at home. Turning it off doesn't hurt it. Unless you leave it off forever. I had a friend with a Volvo station wagon years ago, who was so proud of never running his air conditioning. Then when he tried it it was a goner. The seals had dried out. It's a tad different on our boats. Our fridge is 26 years old, but it only has been "running" less than 5 of those years. It still works.
The last reason is that if the dock power goes out and you're gone for a few days, so are your batteries.
Good luck on the new charger, you'll be amazed at the improvement over one that seemed to have been busted, for whatever reason.
Oh, and hoist a cold one for us, glad we could help.
PS - Here's a loooong discussion about this very subject, from 10 years ago!!!

, if you're interested:
http://c34.org/bbs/index.php/topic,973.0.html