What happens once mining speed gets close to zero?
I think you are confusing two things here: 


Block generation rate
New bitcoins introduced per block


Blocks will always be found at a rate of approximately one per 10 minute. The difficulty of finding a block adjusts itself according to how many people are trying. Simply said, if N people are mining (all with equal hashing power), they will each (on average) find one block per N*10 minutes.

On the other hand, the newly introduced currency in each block is currently 50 BTC/blocks, but somewhere end 2012 this will decrease to 25 BTC. 4 years later, it will become 12.5, and so on. Around 130 years from now, the last block with non-zero new coins will be created. After that, mining will still continue, but blocks will only have transaction fees as rewards, and no new currency anymore.