No, éirigh as fits in a number of ways.

See meanings 2 and 3 here:

http://www.focloir.ie/en/dictionary/ei/ ... p#give__55

It is especially the sense of giving up the habit (meaning 3 above) of dwelling on the past, etc., that is meant by the quote.

That's not to say that there isn't more than one way to express this, but éirigh as definitely fits.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

But 2. and 3. require an action (2 especially) - giving up working, giving up cycling. I think toitíní is really an exception beacause caitheamh na dtoitíní is clearly implied by toitíní in everyday usage. The past/present/future as temporal entities certainly don't quality as actions/habits.

An am atá thart/romhainn/i láthair doesn't alone imply an obsession or need to dwell on/live in said time- we need something more to clarify that, like you say, "the habit of dwelling on" is what is being referenced to when saying "Éirigh as an am atá thart srl."

I can imagine éirigh as working as "rise out of", but not as "give up", but even still "éirigh as an am atá le teacht" feels a little ait, im' thuairim féin...

Ah, yes, I see what you mean now.

As you suggesated above, lig uait "relinquish" might fit better:

Lig an t-am atá caite uait, "Give up the past,"
Lig an t-am atá le teacht uait, "Give up the future,"
Lig an t-am atá i láthair uait. "Give up the present."

_________________
Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).