eucatastrophe: piercing joy that brings tears

[The Squatter of Amon Rûdh]

But if it happens more than once is it still a eucatastrophe?

Since two similar events can be catastrophes, I would say 'yes'. Some eucatastrophic events can be greater and more decisive than others, but that doesn't make the more minor ones any less deserving of the description.

How is eucatastastrophe different from catharsis?

I obtained the following definition from dictionary.com:

ca·thar·sis Pronunciation Key (k-thärss)
n. pl. ca·thar·ses (-sz)
Medicine. Purgation, especially for the digestive system.
A purifying or figurative cleansing of the emotions, especially pity and fear, described by Aristotle as an effect of tragic drama on its audience.
A release of emotional tension, as after an overwhelming experience, that restores or refreshes the spirit.
Psychology.
A technique used to relieve tension and anxiety by bringing repressed feelings and fears to consciousness.
The therapeutic result of this process; abreaction.

[New Latin, from Greek katharsis, from kathairein, to purge, from katharos, pure.]

I would say that a eucatastrophe is an event, whereas a catharsis is an effect. A eucatastrophe may bring about a catharsis, but it doesn't constitute one.