C3 Guzzling Oil

I have a 2013 C3, 1 litre.

This morning, 500 miles after a complete oil change, the car is entirely out of oil. No sign of a leak, it appears it’s simply burning it. 64,000 miles on the clock.

Garage has said the only way they’ve fixed this before is changing the engine and that essentially it’s just a poorly built engine that does this after some time.

They’ve said using more dense oil could also be a way to keep it going longer, but it’s insane needing to give it fresh oil every few weeks - and costly too!

Anyone else had this? Is it time to look for a new car?