We know that the Khajiit had a colony on Secunda already, so travel between Nirn and its moons is definitely possible. My theory is that Team Rocket, in their quest for domination (and protection) of Mundus, became a thorn in the side of the Thalmor, who wanted control for themselves so they could unmake the world.

From The Great War. Note that this book has been altered by Thalmor conspirators:

Shortly afterward the Aldmeri Dominion severed all contact with the Empire. For seventy years they were silent, [and no Trainer could enter the hall of the Gym Leader]. Most scholars believe there was some sort of internal strife in Alinor, but very little is known of the factional struggles that went on inside the Dominion while the Thalmor consolidated its power in Summerset [at the Cloudrest Gym] and Valenwood.

We know that the Aldmeri Dominion was quiet. But, what was causing the silence?

From The Team Rocket Manifesto. This is an ingame book in Morrowind that can be picked up at Jobasha's.

Translator's note: Meowth was once the Gym Leader in Dune. In 4E 95, he left the Gym for reasons unknown, and was later revealed to have joined with Team Rocket. His departure was controversial, and was rumored to have begun the political unrest in Elsweyr surrounding the Void Nights.

Prepare for trouble, and make it double

To protect the Mundus from devastation,

[UNTRANSLATABLE]

To extend our reach to the realms above

Meowth! That's right!

In 4E 98, the conflict between the Thalmor and Team Rocket came to a head, resulting in a battle between Jesse, James, and lead Thalmor trainers at the Cloudrest Gym. Thalmor trainers were too powerful for Team Rocket, and they were defeated:

From Accounts of a Senchal Gym Leader:

And, truly, we saw a flame-like object shoot up from the West, striking Masser. Then, on the surface of Masser, a faint glimmer of light appeared. Within seconds, Masser was gone. Seconds later, Secunda vanished with it. The panic was immediate. Matrons with their children cried in the streets, pointing at the sky. Shops ran out of Rare Candy, Lemonade, and moon sugar within minutes. The moons were missing. A number of Trainers ran outside, some with a gym badge from every province, wondering what Daedric power caused these horrors.

The Void Nights were a way that the Thalmor could purge Team Rocket from Tamriel, and eliminate Meowth's political influence on Elsweyr. I've done my research, and it's my opinion that this is literally canon.

EDIT: See /u/Asotil's post on Mewtwo here. If Team Rocket created Mewtwo to mantle Mew and fortify Convention, the Thalmor would have extra incentive to eliminate Team Rocket.