Actually I was wondering if the batteries had ever been checked before you posted about the one battery being changed out.
Yes one can certainly not only drain but kill the other battery. All of these times you are draining the batteries is seriously decreasing their lives as well even if they were not the issue.
Unfortunately you made a mistake in not getting both replaced at the same time. You will likley need to get both batteries swapped out as you could run into the same thing again with the now weakened newer battery. As a general rule bats set in parallel should always be changed out as a set.
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FYI stuff in case your interested:
Be warned Motorcraft batteries (at least the ones you can get that were not installed at the factory and even those are a step down comparatively to days of old) are not the batteries they were back in early 2K and prior. Until 2002/3 MC were made by GNB. In '03 GNB sold to Exide and Ford was lobbied by and sold the contract to the battery giant Johnson Controls. Quality dropped significantly. They are not the "can go 10 yrs" batteries of old anymore.
My uncle use to swear by Motorcraft batteries and they were great as I recall a few set lasting 10 yrs on his trucks!! On his new Ford trucks he was changing out the MC batteries much more freq with many only going 2 yr and only 1 over 4. He finally switched off off them completely. He runs roughly 15 various trucks along with many tractors and other farm equip.
I am sure most can recall how great the old optima batteries where back in the late 90s and early 2K? Then they went to crap. That happened when Gylling Optima Batteries AB of Sweden sold its company to Johnson Controls. Then JC moved the manf to mexico but of course kept a high price based on the established rep of the original Swedish product. Guess where JC makes the replacement Motorcraft batteries? "Made in Mexico"
Thus Motorcraft is another Optima story.
The one redeeming quality of the Motorcraft batteries Max line is the warranty.
Now it seems the Ford factory new batteries while from JC come out of their Canby, Oregon plant but all the motorcraft replacements are from south of the boarder. This happens with a number of parts these days you pay a dealer premium for the same part the vehicle cam with but get a inferior one.
Basically while the quality can be different for different labels as they are made to their spec JC controls the US battery market along with Exide ( now in bankruptcy protection) and Enersys has a much smaller portion but they supply the US Mil establishment which is a huge % of their....
JC makes:
Interstate, Everstart, Duralast, Kirkland, ProStart, the Gold and lower Die Hard, all of the Motorcrafts and countless "signature" and OEM labels. All kinds of EU battery market as well as they took over German HOPPECKE Automotive GmbH & Co. Another company that at least till then HAD a great rep. Not sure now as they may have required manf to say in EU.
Currently the only "automotive" batteries I recommend are Odyssey/Sears Die Hard Platinum (AGM) which are one in the same battery. Only difference being the case color and sticker. They do cost but the DHP are priced great deal lower than the Odyssey Extreme premium label. These are basically the same as the Hawker Plus line (AGM) for the mil.
There are a few popular named marine batteries at that good but also carry the price.