You are right to purchase a replacement converter and the folks at Best Converter are the right folks to help you on that.
It sounds like you'll keep the replacement right there at the PUP, which is a good thing. It could be a loose solder joint and the warming/cooling of the days could be causing the intermittent functioning. Personally, I would rip and replace it as soon as I could. When things are dying, they generally don't do it for me during the daytime or at the beginning of a window of time that I could work on it. It's at night or right before I need it the most. I did one in the driveway at home but needed nothing more than some needle nose pliers and screw drivers.
The Magnetek is an older converter with really old electronic technology. If you do ever charge phones and computers even when plugged into 120v AC, your devices will like the cleaner power from the Parallax much better. The Parallax does recharge the battery but the documentation does not indicate that it is a "smart" three-stage charger, so I wouldn't just leave it plugged in all the time when in storage.