I have been redeeming lots of trips at the low level without much difficulty. One thing I have noticed that when I enter my travel dates, the tabs for the days surrounding my date only show high availability. But if you click on the tabs, low availability will often appear on specific flights for the date. Have you tried that?

Also, most of my redemptions out of DEN are to destinations with multiple flights per day. I have had trouble with low level awards to PSP, a sub-daily route. I have also been looking for March, which also may account for the lack of low level awards.