If planetary rings are maintained by staying within the Roche limit, how is it that J1407b's rings extend so far? Surely the gravity and tidal forces should be low enough to allow a moon to form.
There are a few ways that a gigantic ring system outside the Roche limit might be possible. Ring systems can extend well past the Roche limit if they are very faint or very young. A faint/light ring system doesn't have enough mass to coalesce and a young system might not have enough time. Young small moons with lots internal heat of formation can be volcanically active too, feeding a ring system.
Saturn's E ring is well outside it's Roche limit.
The most likely explanation for it's enormous and very dense rings, however is that J1407b is very young and a lot of it's ring system will likely to coalesce into moons in time. The breaks in it's ring system suggests that some moons are already clearing paths in it's rings.
It's mass is also very significant. While difficult to estimate, it's thought to be about 10-40 Jupiters in mass. Source. That would give it a mass in the range of 33 to 130 Saturns and a Roche limit some 3 to 5 times (cube root of the mass), distance to Saturn's center, perhaps 6-10 times the distance from the surface surface. Because it's ring system is about 200 times the size of Saturn's rings, the mass alone wouldn't explains part of it. Mostly likely it's a combination of very massive planet/perhaps a brown dwarf star and young plant/star with a satellite system still in formation.
There might also be a very powerful magnetic field at play that helps prevent the ring debris from forming into satellites, but that's just speculation on my part.
There are actually two main ways to form rings, which I'll call the bottom-up and top-down approaches.
In the bottom-up approach, a moon or other body moves inside the planet's Roche limit, and is torn apart by tidal forces. The resulting particles then settle down into a plane and spread around the planet until a ring is formed, of roughly uniform density. Over time, the ring may dissipate and dissolve, or it may grow larger if more satellites are broken up close to the planet.
The top-down approach involves material left over from the beginning of the planetary system. Planets, moons and other bodies form from the protoplanetary disk early in a system's lifetime, and coalesce from smaller fragments. More massive objects rich in volatiles grow bigger and become gas giants. They then further dominate their part of the planetary system, and may accrete more matter after they have finished forming. This matter can create a large ring around the planet, without any need for satellites.
This is the current hypothesis about how J1407b's rings formed. Kenworthy & Mamajek (2015) write
This eclipse and model imply that we are seeing a circumplanetary disk undergoing a dynamic transition to an exosatellite-sculpted ring structure, which is one of the ﬁrst seen outside our solar system.
This circumplanetary disk is likely a leftover from the system's original protoplanetary disk. It may also be leading to the formation of an exomoon.