I too had a problem with the site once recently and ended up with multiple postings. What I discovered was that if the web lackys are doing anything with the site it'll freeze the attempt at posting, causing a repeated attempt, and then when they're done multiple posts will occur.
Now, to the question: Hyundae just does not want to bother. Technically, since it was reported while still under warranty, they're obligated to fix it under warranty.
But if it were my daughter I'd take it straight to a reputable independantly owned and operated shop. The heck with Hyundae, there's a daughter-safety issue at stake.
This problem is diagnosable. This should have stored fault codes in the ECU. These can be read by the willing. Beyond that, various ignition components that commonly cause these symptoms can be tested for susceptability to heat failure.