If the sandtrouts turn water into a pre-spice mass resulting in desertification, wouldn't the water source deplete, which would stop the production of melange? Then the sand plankton, which feed on melange, would die out, destroying the Spice Cycle. If not, what reproduces the water necessary to the Spice Cycle?
They don't turn water into spice. The spice is a complex chemical dissolved in the water. That's why it can be dried and compressed into disks used as money in the deep desert.
The water is recycled from the sand plankton to sand trout to sand worms through the atmosphere and underground aquifers. This is explained in the appendix of the first book.
I would guess that the sandtrouts are not able to completely encyst all moisture when they form the pre-spice mass, so some water leaks out of the process and is available for the next cycle.
Also, while sandtrouts and sandworms are the dominant biology on Arrakis (or other spice planets later in the series), there is still other life on these worlds, and so it is conceivable that water is introduced into the system by other means (as a by-product from some bacterial process or something - I imagine a rotting sandworm could release a lot of hydrogen in molecular and compound forms).
It is also possible water-laden meteors and comets could introduce new water every so often - they don't even have to be all that large if they are mostly ice and hit regularly - most of them would burn up. However, I can't recall any meteor strikes being discussed in the books, but I would be surprised if it never happens.
There is also a large amount of water locked up at the poles - it could well be that these polar caps have been diminishing steadily over time, providing enough moisture to sustain the spice cycle.
Finally, humans have big spaceships that are capable of instantaneously travelling from one world to another - it isn't inconceivable that water is shipped in from worlds where there is an abundance. This is also not discussed in the books - and given the importance of 'planetologists' in the Empire, it might be that they don't do this too much as removing that much water from any other world would seriously disrupt that world's ecology and the humans know this. Then again, some powers (like House Harkonnen) don't really care about their planets' ecologies (look at Giedi Prime).
The question assumes a closed system in the spice cycle - but there are plenty of routes for water to be re-inserted into the cycle.