If you have a phone charger handy, check if the controllers charge when connected to it. If they don't and there are no issues with the ports or the cables, the safety chipset is disabling the charging process either for safety reasons (Li-ion cell damage) or because it's getting false battery state reports (faulty charging circuit/battery). It's hard for me to diagnose the issue without seeing the controllers themselves, but since both are experiencing the issue simultaneously, I expect it to be related to the cables you're using or the console itself rather than the controllers. Like I said, use a phone charger - a 1A plug should be more than ample for a fast charge. Once the controllers are sufficiently charged, the circuit should switch to trickle charging again, which will probably resolve the problem. If not, look into buying spare batteries and charge boards - thankfully the PS4 controllers are modular and parts are relatively cheap. If all your attempts fail, you might need new controllers, although that's unlikely.
