Which species of Phytophthora are you using? For some motile zoospores will only emerge when they are fresh. Otherwise the zoosproes will encyst inside the sporangia and often germinate directly from the sporangia. Caduceus sporangia are likely to be viable without germinating for longer unless they get moist warm conditions. Again depends on species.
Having said that +/- 3 hours isn't going to affect most species especially when maintained in liquid medium that they were grown in.
Hyaloperonospora arabidopsidis spores from sporanghia are particularly weak. I have tested for viability immediatly after harvesting into cold water and 3 hours later with trypan blue staining. Viability is less than 100% (since some sporanghia have emerged earlier than others and are therefore older) but drops down to less than 30% within 3 hours in water. But remember that we maintain this pathogen in the plant and not on agar plates.