@KimberlyMcCallum Hi Kimberly! This was my original post to my "Dynamic Choice Lists using Search Appearance" dilemma. Unfortunately, I have not found a solution. I'm thinking the problem lies within the fact each time a repeat record is added, the search() is run and it pulls fields from the feature service all over again, consequently clearing selection of the previous repeat.
As a workaround, I moved the select-one search() questions outside my repeat and added text fields inside the repeat with the calculation set to the select-one questions. If the text field is set to read only it will not recalculate when a new repeat is added and the value within the repeat will reflect what was selected. At least in may case, the functionality of the repeat is now how I want it. But, the select-one question is still selected and there is nothing prompting the user to select a new choice from the list, so it's a little clumsier and not ideal for someone who's not familiar with how Survey works.