Short answer? Not all postpositions require declension of the noun they are modifying. In other words, the noun they modify remains in its "nominative" or "absolute" case. "Sırasında" is one of those postpositions.
By the way, this was a good question and is actually answered by the notes given for this lesson. If you're like me, you read through the notes at the beginning of each lesson, but either you read through them too quickly and don't full absorb everything, it's too much to take in all at once, or you just simply forget. Either way, I always find I get a lot more out of them upon a second or third read spread out over time. You can access the lesson notes for this lesson at the link below:
Also, once you have started a lesson, you can click on "Tips & Notes" and a window with the lesson will pop up without making you have to exit the lesson.
Hope that was helpful to you.
It's kind of like saying "In the summer's duration", I think. Breaking it down:
• Sıra - Sequence, order. I guess it can be seen as duration as well(!). This would be the root word.
• Sırası: sıra + sı (possessive 3rd person suffix) - Something like "duration's" or "while's", in this context.
• Sırasında: sıra + sı (possessive) + n(buffer letter(!!) ) + da(locative suffix) - "In the duration's", more or less.
(!) More on sıra's meaning: http://www.turkishdictionary.net/?word=s%C4%B1ra
(!!) The buffer letter N is used for words who have already been suffixed.
(note: I'm still learning, all of this is just a guess)