What was once misplaced need not necessary be forever lost
When distracted by food, things sometimes go missing.
The desert might be vast, but the area of search could be drastically reduced when searching for a lost item methodically.
Prior to the start of the search it is important to figure out the bearings of the camp so that you yourself become the misplaced item. Do so by identifying 3 distinct landmarks that are visible all around the desert.
Start your trace by cutting the traversed path in half and doing search along the section of the path in which item was most likely misplaced. Check for wind direct to determine maximum potential distance fallen misplaced item could have drifted away from path traversed.
To trace the route of traversal accurately, identify footprint/paw signature that you will track through the sands. With each step scan within area misplaced object will most likely fall footprint/paw signature.
Bring lots of water while conducting this exercise to ensure against other complications like dehydration during operations.