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This requires some exposition, so please bear with me...

Under the rules for Conjuration (Summoning) the PHB has this to say:

"A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can't be summoned again."

I checked and this exact wording is taken from 3.0 Edition, indicating that this existed prior to the introduction of the Eidolon class features of the Summoner class.

In the Summon Monster spell, it says:

"The spell conjures one of the creatures from the 1st Level list on Table: Summon Monster. You choose which kind of creature to summon, and you can choose a different one each time you cast the spell."

The Mount spell has nothing so say via it's limitations.

My question is, if I summon a mount with the mount spell and it 'dies', does that mean I cannot use that spell again for 24 hours?

Additionally, if I summon a dog with Summon Monster and it dies, does this mean that I have to choose a different animal type if I cast the spell again?

Any help will be much appreciated. Thanks

For reference: Rescued from Purgatory

PC got herself turned into a frog and lost on the Astral Plane.

My thoughts are that someone picked her up and now has her. Other PCs have to find then rescue her before they lose track of her forever.

Is there a published adventure that could be adapted for this purpose?