Dropdown sign doesn't show up in the Select field when Multiple Values = Yes


I have a weird problem in the Search app. When I use search field of type Select with Automatic Lookup where SQL statement returns original(int) and lookup(text) values and Multiple Values=Yes, the drop-down button (small triangle, enclosed in the square) doesn’t show up, therefore drop-down list doesn’t show up either and scrolling is available only within the narrow original field’s space, which is very uncomfortable. If parameter Multiple Values=No, everything works fine.

Interesting thing - if the correspondent field in the main table contains real text values (not integer keys, taken from the lookup table) and SQL statement in the search field returns text values from the lookup table, everything is OK.

Meanwhile I bypass the problem using Double Select fields for Multiple Selection, but this looks ugly if you have more than two search fields.

Any ideas how to avoid the issue?