I think that sankharas arise and cease -- they arise dependent on other things, created from or of other things, when and only when other things exist -- and they may cease when those conditions (dependencies, components) change or cease.
Conversely nibbana is defined as "unconditioned", and therefore isn't a sankhara (it's a dhamma), and isn't siubject to arising and ceasing -- it's not impermanent, not anicca.
I don't know what the doctrine says about the word "eternal" -- it says that "the dhamma" is akalika (meaning "timeless" or "without time", possibly "immediate" or "ever-present", I don't know about "eternal"). I think that "dhamma" used in that sense (to refer to Buddhist doctrine) isn't necessarily the same as saying that nibbana is a "dhamma" rather than a "sankhara" -- apparently "dhamma" is a word with several meanings/uses.
In SN 56.11 it's not "dhamma" that arises but rather dhammacakkhu or "insight into dhamma" which is associated with "stream entry".
Whether that is eternal is another matter.
Think carefully the conditioned (arising dhamma) comes out of the unconditioned (nibbana). Without the unconditioned there is no conditioned either.
You might find doctrine like that in Mahayana schools, e.g. (I don't know) Nagarjuna.
Also some schools of Buddhism (e.g. Tibetan) say that nibbana is temporary too, though apparently that sounds contrary to e.g. the doctrine of the Pali suttas.
For Mahayana doctrine you might want to look at topics such as:
I think it's contrary to Theravada doctrine, though -- perhaps because Theravada defines nibbana as a state in which defilements and so on don't ever arise, will no longer ever arise, never arise, cannot arise, in which the conditions for their arising don't exist (like a palm tree which has been cut down doesn't regrow).
There's some complicated doctrine though about whether nibbana is a state of mind, based on whether how it's perceived by an arahant -- see e.g. this footnote:
Some have objected to the equation of this consciousness with nibbana, on the grounds that nibbana is nowhere else in the Canon described as a form of consciousness. Thus they have proposed that consciousness without surface be regarded as an arahant's consciousness of nibbana in meditative experience, and not nibbana itself.
I'm not sure whether or why that's a doctrinal distinction worth making, though.