Is it possible for you to use the input field without an id or name attribute? Without that, the browser doesn’t really have any way to associate a history with that element.
In my real quick testing on Firefox, this seemed to do the trick:
<form>
<!-- these will remember input -->
With id: <input id="myInputId" list="myList" /><br />
With name: <input name="myInputName" list="myList" /><br />
<!-- these will NOT remember input -->
No id, name, class: <input list="myList" /><br />
With class: <input class="myInputClass" list="myList" />
<datalist id="myList">
<option value="Option 1"></option>
<option value="Option 2"></option>
</datalist>
<br />
<input type="submit" />
</form>
In the code above, the inputs with an id or name would remember past values, but the input without anything and the input with just a class would not remember anything.
Unfortunately, this does make using the input slightly more difficult if you need it to have a name or id. In that case, I’d try having an id‘ed input which is also display: none‘ed and then use some JavaScript to keep it in sync with an input that won’t remember past values.