We frequently carry hard boiled eggs for up to three days. So if I cook them on a Tuesday for a hike starting on Wednesday, we'll eat hard boiled eggs on Wed, Thurs, and Friday. That's assuming night-time temps below 50 and day-time temps below 75. If it's a hot hike, say 80 or 90, then we only carry eggs for the first day. For an October trip in the Sierra, where it's below 40 at night and below 60 during the day, I'd not hesitate to carry hard-boiled eggs for 4 or 5 days.
Jim carries all the food that can get warm, and I carry all the food that should stay cool (cheese, chocolate, eggs, roast beef, hummus, carrots, dolmas, etc). I pack that sack of food with at least an inch of insulation all the way around, nested inside down jackets and such.
We always get an early start, so the food bag is insulated before the sun has warmed the air, and I don't take that sack out at all until evening; the food we need during the day is packed in a separate bag. I carry the double down quilt and both down jackets, so I've got a LOT of insulation to work with, so my pack volume is 2x Jim's pack volume, since he has dense stuff and I have all the insulation.
This whole packing strategy was established to prevent melted chocolate. But now that we've got the system, we take fresh food like this for the first 2-3 days of almost all our hikes.