Stamp 4 travel

My wife has a stamp 4, she is a mexican citizen, but a US LPR, so went back to get her citizenship, so that she can visit her family in the states with ease, as she would lose her Greencard if she stayed out of the US, so this just makes sense.

How long can she be out of Ireland, as its going to be probs over 6 months she will be out in total :/ - can they tell what date she left the country, will she be refused back in, or just have to apply for the stamp 4 again (we're not too worried about that) just want her to be able to come back after she gets her US passport.

Thanks,

Tim