MKR GPS Shield library only works if you call GPS.Available() non-stop

You do not have a problem. It's how it all works.
See, functionally the same as your code:

////////////////////////////////////////////////////////////////////////////
void fGPS_Parse(  void *pvParameters )
{
  // int iBit = 1;
  for (;;)
  {
    xEventGroupWaitBits (eg, evtGPS_Parse, pdTRUE, pdTRUE, portMAX_DELAY) ;
    if ( xSemaphoreTake( sema_GPS_Gate, xTicksToWait0 ) == pdTRUE )
    {
      //query GPS: has a new complete chunk of data been received?
      if ( GPSSerial.available() > 1 )
      {
        if ( GPS.encode(GPSSerial.read()) )
        {
          if (  GPS.location.isValid())
          {
            if ( xSemaphoreTake( sema_Posit, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xPosit.Lat = GPS.location.lat();// store data into structure
              xPosit.Lon = GPS.location.lng();
              xSemaphoreGive( sema_Posit );
            }
          } // if (  GPS.location.isValid())
          if (GPS.speed.isValid())
          {
            if ( xSemaphoreTake( sema_Posit, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xPosit.MPH = GPS.speed.mph();
              xPosit.KPH = GPS.speed.kmph();
              xSemaphoreGive( sema_Posit );
            }
          } //  if (GPS.speed.isValid())
          if (GPS.time.isValid())
          {
            if ( xSemaphoreTake( sema_Time, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xTime.iSeconds = GPS.time.second();
              xTime.iMinutes = GPS.time.minute();
              xTime.iHours = GPS.time.hour();
              xSemaphoreGive( sema_Time );
            }
          } // if (GPS.time.isValid())
          if (GPS.date.isValid())
          {
            if ( xSemaphoreTake( sema_Date, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xDate.iMonth = GPS.date. month();
              xDate.iDay = GPS.date.day();
              xDate.iYear = GPS.date.year();
              xSemaphoreGive( sema_Date );
            }
          } // if (GPS.date.isValid())
          if (  GPS.altitude.isValid() )
          {
            if ( xSemaphoreTake( sema_Posit, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xPosit.Alti = GPS.altitude.meters();
              xSemaphoreGive( sema_Posit );
            }
          } //  if (  GPS.altitude.isValid() )
          if ( GPS.course.isUpdated() )
          {
            if ( xSemaphoreTake( sema_Posit, xSemaphoreTicksToWait ) == pdTRUE )
            {
              xPosit.Hdg = GPS.course.deg();
              xSemaphoreGive( sema_Posit );
            }
          } // if ( GPS.course.isUpdated() )
          if ( xSemaphoreTake( sema_Posit, xSemaphoreTicksToWait ) == pdTRUE )
          {
            xQueueOverwrite( xQ_Posit, (void *) &xPosit );
            xSemaphoreGive( sema_Posit );
          }
        } // if ( GPS.encode(GPSSerial.read()))
      } // if ( GPSSerial.available() > 0 )
      xSemaphoreGive( sema_GPS_Gate );
    }
  } // for (;;)
  vTaskDelete( NULL );
} // void fGPS_Parse(  void *pvParameters )

It's how it works.