Here the speaker begins to personify nature. In other words, some of the smack talking he’s doing about summer sounds like he’s talking about a person.
Basically, strong summer winds threaten those new flower buds that popped up in May, and summer just doesn’t last very long.
The way he describes the short summer, though, is what’s interesting. Summer has a "lease" on the weather, just as your family might have a lease on your car; like a person, summer can enter into, and must abide by, agreements.
The point here is clear enough: the summer is fated to end.
But check this out: isn’t summer also fated to begin every year once again? Can the summer possibly have "too short a date," if it happens an infinite number of times? Isn’t it, in a meaningful sense, immortal?
Keep this in mind as you read on.