11.5 volts??? Your battery is dead. Force it to go lower and you're severely damaging the cells and they'll hold less and less charge and go dead much quicker. You need to upgrade the battery bank capacity (available amp hours).

11.5 volts??? Your battery is dead. Force it to go lower and you're severely damaging the cells and they'll hold less and less charge and go dead much quicker. You need to upgrade the battery bank capacity (available amp hours).

Not exactly Ric, deep cycle batteries are designed just for this. That said, the OP did not mentioned the type of batteries installed.
My cockpit fridge is a Waeco and it does the same thing, I installed another deep cycle (I now have 2 group 31 deeps for the ship alone) and the fridge still shuts off after a couple hours while the cabin fridge (different manufacturer) can run for 24 plus hours.

I called Waeco to see how to over ride this a couple years ago and they would not tell me, said it was there to protect the compressor

Had this issue on my fridge in the cabin as well. Was told by Nova Cool that Four Winns specifically did not run heavy enough wire to the fridge, which causes the voltage to drop below the shut down thresh hold during compressor startup (I witnessed this as well on my multi-meter), and that the only real fix is to run heavier wire. I did the jumper fix initially, and that did prolong my fridge time but not much. Finally broke down and ran a new heavier wire and breaker, and now, it runs forever.. If I were you, I'd just run the new wire... It was not a fun task, and I was a bit perplexed as to why they actually ran the wire like that (it really added to the length, but also explained partly why they had the issue).. They ran 14ga wire to it, and according to Novacool (and most wiring people probably), for the draw and length of travel, needed 8-10 ga. I ran 10ga, and don't see the drop now on the Multi-meter..

I'm not convinced that new batteries will do the trick. The wiring is still likely the root cause of the problem. The bypass, if it is the same as what mine was, only lowered the cutoff voltage 1 volt or less, so, in my case, because of the wiring, it would still drop below that cutoff point after a short time on batteries. I've added extra sets of batteries to my boat, and should have the battery capacity to run my fridges at minimum 2 days without starting a motor or generator, but I wasn't even getting 4 hours. After the wiring switch, I've yet to have it shut off during a weekend on the hook, mildly running the stereo, and also running the cockpit fridge to keep the beer cold (which never has had the problem mentioned in this thread, but is a Norcold I believe)..

Bliss, I just retraced the original wiring from the control panel in the cabin, to the fridge. The wiring to the control panel, is apparently heavy enough... However, the fridge is on the opposite side of the cabin from the panel, and to do that run, they went all the way around to the stern, through the engine compartment, and back up the other side.. I followed the same route, and with a lot of cussing, got it done. I wouldn't have gained a whole lot if I just went straight to the battery switch as you spoke, so I just kept it "stock" so to speak.. If you have that close of a shot, I would probably do as you're suggesting, for the simple fact, the shorter the run, and the less stuff in the run (breakers and switching and what not), the better off you'll be. Ideally, the more direct you are to the batteries, the better wiring wise, but you also have to make it manageable for purposes like you mentioned...