I've been having a lot of bother with my Reactic+ (which I was given as a present) - it's flat every time I check it before packing.
I googled Petzl Reactik+ doesn't hold charge and immediately found this thread:
https://www.ukhillwalking.com/forums/gear/petzl_reactik+_not_holding_charge-69...
I'd have posted on it, but it's archived.
Anyway, I just wanted to mention it in case others have the same problem. I haven't noticed the green LED flashing away after charging, but it might be and I'll check it after it charges this time - and try turning it on and off again too, to see whether that helps for this weekend. I'll try to remember to post back and say whether that helps.