The only way to tell for certain is to fill it, charge it and get one of those hydrometers that test the acidity of the mixture on all the cells and tells you if the cell is weak or dead. If any of the cells are bad or weak, the whole thing should be replaced.
Someone told me long ago never to let them get low, let alone let it run dry. I would err on the safe side and say you could have a problem, but only testing each cell will tell for certain.
Also, you can bring the battery to a shop and they could test it too...but take it to a trusted shop.
Simply because it works now does not indicate how long the charge will last. Worst place to find out is when your out camping.
I would say yes because I too had A dry battery. I filled it up and put on a charger and it would not hold a charge. So I would say it is time for a new one.
As I understand it, letting a battery run dry or sit uncharged for long periods of time results in sulfation, where a compound forms on the plates which cannot be removed by normal charging. A few years ago I was researching off line power for homes and there was much excitement in the solar power industry over inexpensive equipment which would reverse or revive sulfated batteries. I haven't kept up with this but it might be worth a little web searching.
The other thing to consider is why the battery was dry. The same could happen again if you put in an expensive new battery. It's possible that the battery was never maintained, and neglect is the cause. More likely is that your converter/charger is charging at too high a rate for too long, causing boiling away of the electrolyte. Standard converter/chargers are crude and cheap. The charging rate is typically too low for rapid charging of a flat battery, but too high for maintenance of a charged battery.A modern intelligent converter/charger/maintainer has 4 levels of charging, automatically selected. A brilliant site to understand this is phrannie.org, where you will see recommended two books on 12 volt systems. The site is run by Fred and Annie, long term full-timers, and their knowledge and experience has helped me greatly to enjoy a reliable Airstream. A popular replacement for the charger/converter is the Intelli-power, with the Charge Wizard attachment, which intelligently selects from the 3 charging rates, and engages the 4th de-sulphation mode every 21 hours. If you buy the $40 digital voltmeter that Phrannie recommend (I did), you will be able to check out your converter/charger. The voltmeter has 20 amp capacity, so you can chack your trailer brakes.. Good luck. Nick.
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Nick Crowhurst, Excella 25 1988, Dodge Ram 2500 Cummins Diesel. England in summer, USA in winter.
"The price of freedom is eternal maintenance."
Thanks folks, very much, for all the assistance. I will follow your advice on a go forward basis.
The thing that gets me is that we just picked up this trailer and had a so-called full systems check at a local reputable RV dealer (not an A/S dealer though), and they said all was well. Two weeks later I have an electrical problem. Hmmmmmmmmm?!