Use it to your advantage. The other day I saw availability on Saaver level, but it did not show on BA.com. So I called them up. She looked for me and saw no availability at all. I knew that BA showed availability, just the exact flight i wanted was not showing. Rather than tell her that she was doing something wrong, I asked her to check the next day instead. Nothing. OK, check the following day. Nothing. I went through a bunch of days and she kept finding nothing. I explained that something must be wrong, as there is always availability on this flight. After a few holds, she booked me on the flight that was showing on AA, with a $43.00 or something like that tax& surcharge. Took a few more holds for her to get it down to $5.60. The whole time i was nervous that by fighting over the $40, I was going to loose my flight, but in the end it all worked out!