As I posted in a similar thread:
Update, found a good fix for this..... squeeze the shell (closed) on the charger end (male) plug just a bit. Now with a magnifying glass and a sewing needle gently and slighly pry up the 2 pairs of outer tensioning devices on that charger cable male plug to restore and even augment their original spring action.
Guarantee if your phone port is worn this will help noticeably if not fix it altogether for awhile. Then do it again.
(PS don't forget to clean the phone port contacts removing the battery first of course)
Now I can wiggle it around at will light stays on, and lights up first time every time when you plug it in.
This has solved all my charging problems as you are also experiencing. The female plug on the phone is experiencing wear and the shell expands and gets sloppy. You can compensate by doing the above measures to the charger end of the connection.