I had the same problem when I tried to book a ticket from Berlin to Lima on Latam Peru. I kept getting error messages, and like OP, I once managed to get to the 3D Secure page and approved the payment, but still it was rejected in the end. However, I can buy tickets for domestic flights without an issue. Interestingly, Latam New Zealand and Latam Australia have the same fares as Latam Peru. I have used them to book domestic flights in Peru as well, but I also got error messages while trying to book the BER-LIM flight. The website seems to reject non-Peruvian cards. My friend located in Peru recently booked a flight from Peru to the USA but had to use his Peruvian card for payment rather than a US card, as the payment was rejected otherwise. Because of this, I suppose a VPN for Peru may not work. You may try other travel websites, but they need to be located in Peru, as the lower fares most likely have the point of sale restriction.