Solar Battery Charging
A portable 12V Solar panel should be enough to keep a battery charged, or even to charge a battery given a number of days. However, the wattage you would need to charge a low battery to full (or close to it) in a day or less... Would be so large, that you would not be able to use a portable power system.
Most portable solar panels are under 20 watts.
What you are looking at here is a Watt Hour issue.
Hoe many watts are being used for how many hours.
For example. (A Watt = Amps * Voltage) I have a marine battery that has 85 Amp Hour Rating. The battery is 12V. So I have a capacity of 1020 Watt Hours of electricity available. (If you use 100 % of the charge, which you NEVER should!)
Lead Acid batteries, even "Deep cycle" batteries are damaged when discharged more than 50% of their capacity. You should try to never get them below 50% of their full charge.
If you test the battery's voltage when it is not being used, the below voltage indicates the remaining charge approximately. (Note that this varies slightly with the temperature, and the age of the battery... But we're talking 10ths of a volt here.. These numbers are for a good, but worn in battery.)
% Charge Voltage (Disconnected)
Note that if your voltage ever drops below 11.5 volts, your battery is worse than dead... It is permanently damaged. You should Google "Lead Acid Battery care" if you are interested in more info about how to take care of the lead acid battery.
So based on the voltages you gave, I'd say your problem is that your batteries are damaged. You should give some thought about what capacity battery (or an array of batteries) you need to provide the Watt Hours you are looking for for your power needs. You may want to install several batteries in parallel to get the capacity you need. (Be careful when doing this!)
You may have damaged your batteries by over draining them, especially if this has happened repeatedly.
How big of a solar panel do you need to charge your batteries? You need to charge what you use in Watt Hours. (Plus a minimal trickle drain.)
Here's the important part.
AH * V = WH
Let's assume you get a new 85 watt hour battery, and plan on using 50% of it's charge capacity so you don't kill it.
If you are charging 50% of an 85 AH battery that is 12V - you need 510 WH.
With a 20Watt Portable Solar panel this means you have to charge it for
25.5 Hours of Sunlight or about 3 summer days of reasonable sunlight strait.
If you want it done in 4 hours? You need (510 / 4) watts or about 127.5 watts. You can buy a 125 watt solar panel on amazon.com for about $700 right now. You'll want to get a charge controller with that for $30-50. But the size and weight of that panel would put it well outside of the "portable solutions" range.
I'm guessing the Watt Hours you would need for this would require a system that is bigger and more expensive than you would be interested in for this application.
Maybe you should put an alternator on your boat to keep the battery charged while you have the motor on.
For remote charging that kind of Watt Hour power... I think you'd want to get a generator and a battery charger. (Or a unit with both together.) Just check out the Amp Hour rating of the charger, and do some math to see how long it will take to charge.
Maybe the info above will help you make your decision on what to do.
I hope this helps.
Jon from Kalamazoo