I believe oocysts can live for quite a long time outside the body, well over a week, this is why they can be transmitted by water (e.g. crypto, giardia)
Oocysts are notoriously difficult to kill, especially Crypto, even bleach may not kill it.
But don't let this get you alarmed, most likely your babies just have worms. During treatment it is neccessary to sterilize the enclosure thoroughly after every treatment, more often if possible. Switching between sterilite containers using papertowels for substrate and deli cups for hides makes this much easier.