It didn't decline.

In Joan Rimmer's "The Irish Harp", she describes the years just after 1600 as the period of greatest development of the Irish harp, but significantly, in a non-traditional direction that made it more suitable for playing early Baroque music. That being what the Irish aristocracy now wanted to listen to, they wouldn't have been very interested in continuing to employ performers on an instrument that could only play an outdated repertoire.

As far as repression goes, she simply alludes to harp song being forbidden within the Pale, and from what she says about how the Irish harp continued to be made and developed both within Ireland and beyond it, there can't have been any serious attempt at systematic suppression. (Compare it with what happened in Chile in 1973 - the generals killed Victor Jara and would have killed a lot more leftist singers if they could have got hold of them, but the CIA didn't attempt to ban the guitar).