I'm not sure what you call "a few days" but Sam and Frodo carried their share of the Lembas from Lorien for about forty days, though they didn't eat it all the time.
I assume the Fellowship ate little Lembas for the first ten days, from Lorien to Parth Galen. Lembas was intended for emergency use so they must have carried other food as well. When the Fellowship split up, Frodo and Sam would have taken their share of what was left of that food, so to start with, they wouldn't have to rely on lembas alone.
When the hobbits met Faramir they were given more food, which they ate until they reached Cirith Ungol.
They had nothing but lembas for the last twelve days to Mount Doom.
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