Bold text is defined by CSS for some elements. When the popup is opened for the first and second time everything appears correct. When the same popup is opened for the third time all text elements appear with plain font - nothing is bold any longer. Please find the test below.

public class CSSDatePickerTest extends Application
{
  public static void main(String[] args)
  {
    Application.launch(args);
  }

  @Override
  public void start(Stage stage)
  {
    System.err.println(System.getProperty("javafx.runtime.version"));
    Application.setUserAgentStylesheet(getClass().getResource("/test/datepicker/style.css").toExternalForm());
    
    Parent content = createContent();
    Scene scene = new Scene(content, 500, 500);
    stage.setScene(scene);
    stage.show();
  }
    
  private Parent createContent()
  {
    VBox vbox = new VBox(10);
    vbox.getChildren().add(createDatePicker(false, false));
    vbox.getChildren().add(createDatePicker(true, false));
    vbox.getChildren().add(createDatePicker(false, true));
    return vbox;
  }

  private DatePicker createDatePicker(boolean showWeekNumbers, boolean disabled)
  {
    DatePicker dp = new DatePicker();
    dp.setDisable(disabled);
    dp.setShowWeekNumbers(showWeekNumbers);
    return dp;
  }
}

style.css:

 .root {
-fx-font: 11 Tahoma;
    -fx-text-fill: black;
}

 .text {
    -fx-text-fill: #F00;
    -fx-font-smoothing-type: lcd;
}

.combo-box-base > .arrow-button {
   -fx-background-color: red;
   -fx-padding: 0 4;
  }

.combo-box-base > .arrow-button > .arrow {
    -fx-background-color: black;
    -fx-background-insets: 0 0 0 0;
    -fx-padding: 2 4;
    -fx-shape: "M 0 0 H 7 L 3.5 4 z";
}


/*******************************************************************************
 * *
 * DatePicker *
 * *
 ******************************************************************************/

.date-picker-popup {
    -fx-padding: 1;
    -fx-background-color: lightgray;
}

.date-picker-popup > .month-year-pane {
    -fx-padding: 4;
    -fx-background-color: #EFEFEF;
}

.date-picker-popup > .month-year-pane > .spinner {
    -fx-spacing: 4;
    -fx-alignment: CENTER;
    -fx-fill-height: false;
}

.date-picker-popup > .month-year-pane > .spinner > .spinner-label {
    -fx-font-size: 1.083333em;
    -fx-alignment: CENTER;
    -fx-text-fill: #606060;
    -fx-font-weight: bold;
}

.date-picker-popup > .month-year-pane > .spinner > .left-button {
    -fx-padding: 4 6;
    -fx-background-color: gray;
}

.date-picker-popup > .month-year-pane > .spinner > .right-button {
    -fx-padding: 4 6;
    -fx-background-color: gray;
}

.date-picker-popup > .month-year-pane > .spinner > .button > .left-arrow {
    -fx-background-color: red;
    -fx-background-insets: 0;
    -fx-padding: 0.333em 0.167em 0.333em 0.167em;
    -fx-shape: "M5.997,5.072L5.995,6.501l-2.998-4l2.998-4l0.002,1.43l-1.976,2.57L5.997,5.072z";
    -fx-scale-shape: true;
}

.date-picker-popup > .month-year-pane > .spinner > .button > .right-arrow {
    -fx-background-color: red;
    -fx-background-insets: 0;
    -fx-padding: 0.333em 0.167em 0.333em 0.167em;
    -fx-shape: "M2.998-0.07L3-1.499l2.998,4L3,6.501l-0.002-1.43l1.976-2.57L2.998-0.07z";
    -fx-scale-shape: true;
}

.date-picker-popup > * > .cell {
    -fx-padding: 0 7;
    -fx-alignment: BASELINE_CENTER;
}

.date-picker-popup > * > .cell:disabled > * {
    /* This is set on the cell's children so the border is not affected. */
    -fx-opacity: 0.4;
}

.date-picker-popup > * > .week-number-header-cell,
.date-picker-popup > * > .day-name-cell {
    -fx-font-size: 0.833333em;
    -fx-padding: 0;
    -fx-text-fill: #0070C0;
    -fx-font-weight: bold;
}

.date-picker-popup > * > .week-number-cell {
    -fx-font-size: 0.75em;
    -fx-padding: 0;
}

.date-picker-popup > * > .day-cell {
    -fx-text-fill: black;
    -fx-border-color: lightgray;
    -fx-border-width: 1;
    -fx-border-insets: 0;
}

.date-picker-popup > * > .hijrah-day-cell {
    -fx-alignment: TOP_LEFT;
    -fx-cell-size: 2.75em;
}

.date-picker-popup > * > .day-cell:focused {
    -fx-background-color: #CCE8FF;
}

.date-picker-popup > * > .day-cell:hover {
    -fx-background-color: #EFEFEF;
}

.date-picker-popup > * > .day-cell > .secondary-text {
    -fx-font-size: 1.0em;
    -fx-fill: #ff5050;
}

.date-picker-popup > * > .today {
    -fx-background-insets: 1;
    -fx-border-color: #606060;
    -fx-border-insets: 1;
}

.date-picker-popup > * > .today:focused {
    -fx-background-color: #CCE8FF;
}

.date-picker-popup > * > .selected {
    -fx-background-color: #CCE8FF;
}

.date-picker-popup > * > .previous-month,
.date-picker-popup > * > .next-month {
    -fx-text-fill: #aaaaaa;
}

.date-picker-popup > * > .previous-month > .secondary-text,
.date-picker-popup > * > .next-month > .secondary-text {
    -fx-fill: #aaaaaa;
}