The observed by you behavior is an expected one. When you open the DropDown only the visible items are loaded into the visual tree. So, when the DropDownWidth is set to Auto it takes the width only of that visible items. When you began to scroll the other items are loaded into the visual tree. Because of that when an item with bigger width is loaded the DropDownWidth changes.
What we could suggest you for your concrete scenario is instead of setting it to auto to measure the width of the filtered items and set the biggest one to the DropDownWidth property. For example you could handle the SearchTextChanged event and inside it to find the widest item from the FilteredItems collections and set the DropDownWidth as needed.
Please, check the attached sample that demonstrates that approach.
Hope this helps.
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