Drawer bottoms nearly always "float" in groves in the sides, back and front.
If the four pieces that form the rest of the box become detached from one another the bottom can fall out - especially if there's lots of stuff weighing it down. Happens mostly on self assembly lower-end stuff
Inspect the drawer and try to pull the box apart - if it gives way then it's best to fix it.
A block of wood screwed two-ways in each corner will hold it together - a DIY store will sell little plastic blocks that do the same job.
http://reviews.homebase.co.uk/1494-en_gb/313905/reviews.htm
And if the drawer bottom is flimsy and flexible and you need to overload it for whatever reason then a strip of wood screwed underneath will help to stop it flexing and falling out.
You might also consider gluing the pieces together and weighing them down overnight while the glue sets - use PVA White Glue but do not glue the base - let it float in its groove.
Good luck...
Peccavi, February 2013
