Mining speed will not get close to zero if bitcoin remains on the road of success, because transaction fees will provide enough incentive to mine, even when the block reward (currently 50 BTC) is close to 0 (it halves roughly every 4 years).
To give you an idea what this could look like, let me estimate some numbers: In the year 2026, there might be around 500,000 transactions per block. Even one Satoshi (0.00000001 BTC) fee per transaction would easily suffice to support quite a secure mining network, because that would add up to 0.006 BTC fees and if bitcoin does 500,000 tx per block (that's about the number of transaction VISA does nowadays), 1 BTC would be valued maybe something like 100,000 USD, so those fees would be equivalent to USD 600, roughly the same as the 50 BTC incentive of today. Voilá.
At least that's the idea. Wether or not it will work, remains to be seen.
There is a possibility of network hashing speed going close to zero: that can happen if bitcoin is being abandoned. Then we'll face the problem namecoin is currently facing: The next difficulty retarget takes a very long time to reach (namecoins next difficulty retarget will be around christmas) and transaction speed will be excrutiatingly slow. A possible solution in such a case would be to change the difficulty retarget rules, maybe along the lines of what SolidCoin is doing (more often, allow greater change).