do items you put in footlockers disappear if you leave them there for a while

Have you heard? NPCs steal things.

Mexican Candy has a point.

But to directly answer your question, it is becoming more evident from experiences posted in the forums that most containers do not respawn (unlike FO3 or OB) if it is empty when you first find it, the chances are even better.

To be sure, put something you wouldn't mind losing into it and come back after 72 game hours have passed. You must leave the cell.

Make a new save.
Put the items into a container.
To leave the cell exist the building, enter another house or building would be the best to do.
Wait three full days.
Re enter the building where you left your stuff.
Check the containers.
If gone reload that clean save.

The general really safe containers are.
Sunset sarsparilla crates ( and you can carry these as well ).
Safes.
Fridges.
Ammo boxes.

Those that are prone to respawning are.
Clothes cabinets.
Suitcases ( I've seen the one at the hotel in Novac respawn two games ).
Lockers.
Bins.
However allways test any container out first.

The vast majority of containers in New Vegas do not respawn, unlike in Fallout 3. Of those that do, most are hidden merchant containers that you'll never see in the course of normal gameplay. The only respawning containers you'll likely see are food containers, certain refridgerators and a few other misc ones that respawn with food items.