How can I keep meringue pie-topping from falling?
Ironically, it could be precisely because you're trying to enjoy the meringue on a hot day that is causing it to deflate so quickly. Meringue are extremely sensitive to moisture, and a humid day can wreck your meringue's volume. It's best to make meringue on a dry day. 

However, there are a few things you can do to achieve better stability:


Use fresher eggs. 
Fats are the enemy. Make sure you have zero egg yolk in the mixture. Also, avoid hand contact, as your oils can rub off. 
Make sure the sugar is fully dissolved, because otherwise it attracts moisture. 


Good luck!