Veloster fuel pump issues

Sounds like a fuel delivery issue, alright. A failing fuel pump can definitely cause those symptoms. When the engine stalls, does it happen more when the fuel tank is low? And does the rough running improve at higher RPMs or is it consistently bad? Also, have you checked the fuel pump relay and fuse? A bad relay can mimic a failing pump.

Thanks for the tips. The stalling doesn't seem to depend on the fuel level, it happens regardless. The rough running is consistently bad, no matter the RPM. You mentioned the relay - where exactly would I find that, and how would I test it? I'm no expert, but I'm willing to try.

Okay, consistent rough running regardless of RPM does point more squarely at the pump itself. The relay and fuse are usually in a box under the hood or sometimes under the dash. Your owner's manual should pinpoint the exact location. You could try swapping the fuel pump relay with an identical relay (if there is one) to see if that fixes it, but given all the symptoms, and especially since it doesn't depend on fuel level, I'd put money on a dying pump or a bad connection to it. Given the potential danger involved with fuel systems, I would recommend having a workshop take a look at it.

Right, I suspected as much. Took your advice and brought it to a workshop; turns out a faulty plug connection to the fuel pump was the culprit. New plug installed, and the car is running like new! Total cost was 95€. Thanks for confirming my suspicions and encouraging me to get it checked professionally!