Hi Chrisa!
The right one does have an antenna connected to it's motherboard. Please open the Joy-Con and check if the antenna is still connected properly to the motherboard. This could cause the random disconnects.
Does the Joy-Con work perfectly fine while attached to the Switch?
Could also be the "Broadcom [link|http://www.cypress.com/file/298421/download|BCM20734|new_window=true] Bluetooth 4.1/2.4 GHz Transceiver IC"...
This required soldering plus soldering skills to get it fixed.
To test if it's the battery or not, you can also buy a grip holder with USB-C! While it's connected to the cable and still losing it's connection, it's definitely the blue-tooth messing around.
Good luck! And please let us know how it goes!