Simply put, more days to cover means, other things equal, that the short positions are collectively larger relative to daily liquidity.
Think of a sponge that can hold only so much water. That is daily volume. If you have a small bowl of water (the short interest), two or three sponge-fuls can sop it up. However, a bucket of water would take a lot more sponge-fuls.
Shorts will need to pay up to buy a bigger sponge.
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