Ascend on a permanent isn't a triggered ability and doesn't use the stack. Players can respond to a spell that will give you your tenth permanent, but they can't respond to you getting the city's blessing once you control that tenth permanent. This means that if your tenth permanent is a land you play, players can't respond before you get the city's blessing.

If your tenth permanent enters the battlefield and then a permanent leaves the battlefield immediately afterwards (most likely due to the "legend rule" or due to being a creature with 0 toughness), you get the city's blessing before it leaves the battlefield.

Once you have the city's blessing, you have it for the rest of the game, even if you lose control of some or all your permanents. The city's blessing isn't a permanent itself and can't be removed by any effect.

If you control ten permanents but don't control a permanent or resolving spell with ascend, you don't get the city's blessing. For example, if you control ten permanents, lose control of two, then cast Andúril, Narsil Reforged, you won't have the city's blessing.

A permanent is any object on the battlefield, including tokens and lands. Spells and emblems aren't permanents.