I’ve tested the battery with a multimeter, it’s between 12.3-12.5 when off and the car is locked. When I started the car the multimeter didn’t go below 10v which from Googling suggests it’s ok? It’s by know means a quality battery but it’s not failed me (so far) but I’ll keep a close eye on it. A new battery is £200 odd which I’d rather avoid for now.Dude, try changing the battery. Honestly.
The Stop/Start on my Jaguar XE and XF both stopped working due to a dash camera. The car is smart enough to know the battery is a dud (or in my case being drawn on beyond the specification it left the factory with) and disable things that are additional draws such as emitting RF to find a key and to minimise load such as stop/start.
I wouldn't say Hyundai's are particularly known for it but I imagine they are as sensitive as other marques.
The only other course of action would be the previous owner in his infinite wisdom (I mean seriously, the front page of motors has a chap who had his car nicked through keyless) removed the fuse for the sensor to disable the system totally. Smart.
I’ve tested the fuses, they’re all fine and in the right place. My other car is keyless and they’re kept in a faraday bag. I know it’s a ‘luxury’ feature but it bothers me that it doesn’t work, and it’s kept me occupied during lockdown. I quite enjoy tinkering.