Low-level awards are usually available in very limited quantities at any one time.

For example: If you search for the initial itinerary using the default 1-passenger you may find low-level availability. But when you attempt to purchase the same itinerary for 3 passengers, the award fare jumps to mid or high level. This is because all award fares on any PNR are quoted/sold at the lowest level available for number of requested seats.

For this reason my wife and I typically purchase award fares on separate PNRs for the same itinerary, even if award miles come from the same SM account (usually mine.) Often we have to wait a few days or even weeks between each redemption for additional low level inventory to open up. This is obviously not a strategy recommended for traveling with children. IROPS and seat selection can be challenging also with this approach.