You are describing a market where a "non-storable" (or "perishable") good is traded. This is the (in terms of historical precedent) model of a market, since in the old days, most goods were agricultural, and many amongst them were "non-storable".
The argument behind "market clearing", i.e. that prices will adjust so that all quantity available will be sold, owes a lot to the goods being non-storable. You can observe this today in the so-called "farmer's markets", where if you monitor a day of trading, you will observe that prices go down as the day nears to an end, as suppliers attempt to sell all their quantity.
Why some consumers nevertheless buy early on and so at higher prices, even though they know that later on prices will go down, has to do with
a) constraints imposed on the consumer schedule (say, he has to buy early because he has to prepare lunch), and/or
b) quality considerations: early on the suppliers may give you more room to "pick and choose" item per item, or they themselves will offer the better quality, to justify the higher price. It may be the case that some consumers have a lexicographic preference over a certain threshold of quality, which they expect it won't be around at the end of the day when prices will fall.
On the other hand, some consumers will hold on, given their constraints/preferences. As you can see, the phenomenon of all consumers waiting till "the last minute" presuposes a situation were the consumers are perfectly "flexible", and the quality of the good does not deteriorate with time, but the good looses all its "good-properties", instantly, at the end of its "useful life". In reality quality erodes gradually, in almost all cases.