I can confirm that not only good chargers but also good cables are important to solve charging problems. First, my FP2 with Open FP is unable to steadily charge with a charge-only cable (i.e. a nondata cable). Second, among functioning data cables not all have the same quality. I was having problems with one of them, a generic cable, and then realized that it’s thinner than other OEM cables from Samsung and HTC. The FP2 clearly doesn’t like cables with small wire gauges! Apparently this problem can happen with all smartphones that drain high amounts of current during the charging cycle, and the FP2 is one of those.
To summarize: make sure that you only use the best USB data cables with the largest wire gauges to charge your FP2, and make sure that USB debugging is set to on in the developer options menu.