The country's services sector improved in November but remained close to three-year lows as new export orders contracted for the first time since 2011 in the wake of Britain's vote to leave the European Union.
Investec's Purchasing Managers' Index (PMI) of activity in services moved up to 56 from 54.6 in October.
November's reading was the second-lowest since June 2013, when the country was still working its way through an international bailout.
The index, which covers companies from banks to hotels, has fallen from a 10-year high of 64 in January, with uncertainty following the June referendum vote in its key trading partner weighing heavily.
New export orders fell to a five-year low of 49.8, dipping below the 50 mark that separates growth from contraction for only the second time since 2009.
Investec said that exporters felt the pressure of a weaker sterling, with business services and travel and leisure sectors under particular pressure.
But this was balanced by a stronger domestic performance to leave the new business index at a three-month high, the survey's authors said.
The growth in services follows an improvement in the manufacturing sector to a post-Brexit high in November, in a survey last week.
All in all, while the services sector is clearly not out of the woods yet, it is encouraging to see that the pace of growth for this sector quickened in November," Investec Ireland's chief economist Philip O'Sullivan said.
"Our suspicion is that the worst of the pressures faced by the more external-facing parts of the Irish economy in the immediate aftermath of Brexit has passed," he added.