tl;dr: We just don't know what the spell would have done; Twilight Sparkle chose to take the safe route rather than risk using demonstrably-dangerous magic again.
As far as I know, the one and only time this spell is seen or referenced is the one time it was cast, since it was fixed immediately afterwards. So, that single test case is the only information we have about it's effects. All we know is that the spell causes the Elements to change colors, which cause the ponies to swap cutie marks.
To start with, there's two ways the color swap could be achieved:
- The spell performs some algorithmic permutation on the Elements, based on criteria we don't know.
- The spell assigns each element a new color"at random".
The latter case is easy: each time the spell is cast there is exactly the same odds of it putting everything back to normal, which is
1/5! or 1 in 120. Those are kinda bad odds already, but it gets even worse when you consider the implications of repeatedly casting things, as I explain further down.
(Note: even though there are 6 Elements of Harmony, Twilight's didn't change, so we only have 5 to fix).
In the former, there's a least a chance your idea might work, but we don't know. How stable the permutation process it is depends on what parameters are taken into account when deciding where each mark goes next. If the permutation is cyclical, as you point out (e.g. they always go from pink -> blue -> orange, or balloon -> lightning -> diamond) then yes, just re-doing the process enough times should fix it. But it could be more complex: does it depends on which pony happens to have which element? Does it depend on the combination of shape and color? Can we construct an algorithm that does the swap deterministically for any given state, but has a cycle in it? (I suspect we could but I haven't tried) If so, we could recast the spell an infinite number of times and never make progress.
However, even if we assume best-case that casting 5 more times would fix things, there's some issues with this idea:
- Casting the spell wrought havoc as everyone struggled to conform to their "new" destiny.
- Casting the spell did not take effect immediately: nothing happened until the next morning. That means casting the spell and waiting a whole day (during which there will be the above havoc).
- We're assuming that casting the spell again will do the same thing: the spell's incomplete, so we just don't know.
- We're also assuming that fixing the Elements will fix the cutie marks. That seems a pretty reasonable assumption, but again, it's broken magic, so who knows?
Overall, it seems like Twilight, with her knowledge of magic, and intelligence in general, would be the person most likely to know if casting the spell again is a good idea. This is particularly true given that Spike recommends trying a counter-spell and Twilight rejects the idea: if the spell were it's own counterspell, surely she would have picked up on that.
Rather, she seems to have taken the safer and more reliable route: just fix the damage directly, and don't risk casting a dangerous half-finished spell any more times.