You should NOT use a mattress for a second or third child if :-
1) You do not know its history how it was looked after and how it has been maintained and cleaned
2) If the mattress does not have washable covers and the core is not waterproof protected.
3) If the mattress has the slightest dip or dent, - not supportive.
4) If the mattress is yours and you stored it in the loft and did not seal it in a plastic bag and it is not thoroughly washable, and does not have waterproof protection to the core.
You can use a mattress for another child if :-
1) You know its history and how well it was looked after.
2) The mattress has a protector (preferably wipe clean and or washable) that is waterproof and will prevent body fluids getting to the core foam or springs or coir and lambswool The waterproof protector can sit under a washable cover and over the base.
3) The covers have been washed regularly at 60°c the temperature required to kill dust mites.
4 ) The mattress has no visible dents or dips has been well maintained.
5) The mattress has been stored clean. All covers or toppers protective core cover, machine washable at 60°c . A fixed waterproof protective base cover can be cleaned with an anti-bacterial cleaner like Milton.
If you have bought a quality mattress you will be able to use it again and again provided it passes the 5 conditions above.