Why does the hash-rate change so drastically? I've been watching the global estimated hash-rate, as estimated by blockchain.info.

While it is clearly increasing, it also varies around 20% day-to-day.
Yesterday, it was around 4,325,000 TH/s.
Today, it is 5,688,000 TH/s.

Wouldn't miners want to keep their equipment running 24/7?

That is a lot of hashing-power to go on and offline so frequently.
What is causing this?
The actual hash rate of the network is not (and likely cannot be) known. Blockchain.info and any other website that tells you the network hashrate is extrapolating it from the frequency that blocks are being produced and the difficulty of each block. However, because there can be significant variance in the times between blocks, this can sometimes make it seem like the hashrate is significantly higher or lower than it actually is. This is likely what causes the variation that you see in blockchain.info's chart.