Does the composition of a solution keep changing when being boiled?
It is not a messed up cycle. Let's consider what happens with an example.
If you heat up a mixture containing $10$% ethanol + $90$% water, the mixture boils at $92$°C, producing a vapor containing $50$% ethanol + $50$% water. With this operation the liquid loses more ethanol than water. So its concentration in  ethanol decreases, and it is necessary to heat it up to a higher temperature to maintain the process of evaporation. When about one tenth of the liquid has distilled, the residual liquid contains still $5$% ethanol, and it is necessary to heat it up to $95$°C to obtain and continue boiling. At $95$°C, the vapor emitted contains $35$% ethanol. At $98°$C, the liquid contains still $2$% ethanol and the vapor $20$% ethanol. When the last drops are vaporized, the temperature is $100$°C and the last drops are made of pure water.