Well, if you are comfortable fixing it yourself, try opening it up and troubleshooting the connection where the epilady mates with the charger. Use a pencil eraser or metal potscrubber (steel wool) to shine the contacts up, and if springs are involved to maintain contact, see if you can't get at them an stretch more life into them.
The good news is, you can treat yourself to a new one direct from
gpcare.com, and of course ebay is always an option if the $60 USD cost of a new unit breaks the birthday budget. But hey, treat yourself, who else will?
I hope that helps.